One must practice at different speeds. But one must also understand why one is practising at different speeds. The actual speed is not that important. What is important is the effect. So you will not get a clear-cut answer: half speed is MM=60, say, because this may or may not be the speed that
for you the half-speed effects are going to be in effect.
So:
1. Tempo is variable. Think of it as in speech. Some people speak slowly; some people speak very fast indeed. Still the meaning and the emotions still come through
as long as the tempo is neither too fast nor too slow. If someone starts speaking at a very slow rate, you will not be able to connect the words into meaningful sentences. Likewise, if they speak so fast that you start missing words communication will not really take place. So when approaching a piece of music, the most important question in regards to tempo is to define at which range of tempos the piece will still be effective. And which range of tempos the piece is effective, but its
meaning changes. Again think speech and you will get the idea: Someone speaking frantically fast may still convey meaning, but there will be overtones of danger and urgency in the message, while by speaking slowly a calming effect result. I use to show this to may students by playing for them Bach’s Little prelude BWV 939 first at top speed then at a peaceful and measured tempo. Then I tell them it is a conversation between Bach and his wife and I ask them to tell me what is going on. The fast version is always interpreted as a domestic argument, while the second, slow version is always interpreted as a lovers’s dialogue.
2. With that established, I find useful to practise in six different speeds:
a. The slowest speed at which the piece is still effective. This means a speed at which you could perform the piece and it would still be a valid speed. Bach in particular allows a huge range of speeds, and depending on the tempo you choose, the piece may even sound completely different. A very good example is the Giga from partita no. 1 which some pianists (Gould, Tureck) play at light-speed, while others paly it so slow as to sound a different piece altogether (Arrau). In fact, Arrau is a good example of a pianist that more often then not performs pieces at this lower tempo boundary.
b. The fastest speed that the piece will allow. Practice is (a) and (b) will inform you about what is effective and how much you can stretch the tempo in one way or the other. This will inform your decision of the final tempo at which to play the piece.
c. Faster than the fastest tempo in (b) above. Arrau would recommend this practice trick to his students: to play 1/3 faster than the recommended fastest speed, since in this way you always had a “reserve” of speed, and even at the top speed (b) your playing would look easy and sound effortless. Now, 1/3 here does not really mean 1/3. (The piece fastest tempo is MM=120, so practice at MM=170). That is not the point. For a start you may not be able to play at MM=170 (it may even be impossible) and trying will just make you ingrain mistakes and get injured. It simply means to practise in order to be able to play
faster than you intend to play the piece at its final tempo. If you can play faster than you intend when performing, and yet perfectly and effortlessly, than when you actually perform the piece at your chosen tempo it will be a piece of cake. The corollary here is,
always perform a piece at a slower tempo then the fastest perfect rendition you managed during practice. If you are having trouble with speeds (a), then this piece is not ready for performance.
d. Half-speed. This is not literally “half-speed”. But if you want to take it literally, then what is means is that if the piece is to be played at MM=120, you play it at MM=60. But instead of focusing on numbers, focus on what you want to achieve by doing it. Just like in (c) above, the point was not to play exactly 1/3 faster, but simply faster so that you would have a technical reserve, the point here is to play at such a speed that you have
the time to hear each sound and check each movement making sure everything is perfect. This is a very difficult tempo – it is just below (a), the slowest tempo at which the piece is still effective. At this “half-speed” tempo the piece is not effective anymore. It is still fast enough for you to take advantage of hand memory – so your fingers will carry you through, but it is not fast enough for you to rely on your
musical understanding of the piece. It will be too slow for phrasing (for instance) to be effective. This forces you to know your piece note by note, movement by movement. Which is why this is both one of the most useful practice speeds and one of the most difficult.
You should not try that at the beginning. For this practice speed to be fully effective you should have already pretty much mastered your piece. You should know and have ingrained the right notes, the right times the right fingers and the right movements. The danger of doing half speed too early is that because it is fairly slow
you will be able to get away with defective techniques which will not work at the pieces proper tempo. The main purpose of half-speed practice is to make sure
everything is right by allowing you extra time. A lot of people use it as a license to practise everything wrong. Then they wonder why they can never get a piece at speed. So half-speed, is not literally half speed, but a speed slower than the slowest effective tempo of the piece, and yet not so slow as to destroy finger/hand memory. Another advantage of this speed is that you will be able to
amplify your movements. For instance, certain passages need to be played by using a backwards circular movement of the arm/hand. Played at full speed it looks like the pianist is moving his hands up and down because at speed the amplitude of the movement must necessarily decrease. But in fact he is doing micro-backward circles. At half-speed you will be able to enlarge these movements and ingrain them, and acquire speed not by moving
faster but by moving smaller. So when practising half-speed, remember that one of the purposes is to allow you larger movements. Aim for fluid/smooth/continuous large movements instead of jerky start-stop movements. Half-speed will be the speed that
for you will allow this complex of results to happen: destruction of musical meaning, but not of hand memory; enough time to do everything right. Enough time to enlarge movements. Enough time to
listen to individual sounds as opposed to sounds in a musically meaningful phrase.
e. Slow speed. This is excruciatingly slow practice. How slow? Slow enough to destroy finger/hand memory. The purpose of this sort of practise
is not technical. No one is going to acquire/improve technique by playing slowly. In fact, this is so slow (about a note per second) that correct movements are not so important (but keep to the right fingers and right notes!). The
only purpose of this sort of practise is to develop other kinds of memory apart from hand/finger memory which is notoriously unreliable. So doing this sort of slow practice with the score in front of you completely defeats its purpose. If you can play your whole piece at this slow speed from memory, you know that you have truly memorised it (the slow speed stops you from relying on hand memory and at the same time gives you plenty of time for using other sorts of memory which a fast tempo make impossible to access, like the harmonic progressions and motif analysis)
f. Ridiculously slow speed. Now you spend 10 or twenty seconds on each note. The only purpose for this kind of practice is to explore muscle isolation. See here if you don’t know what I am talking about:
https://pianoforum.net/smf/index.php/topic,4145.msg38568.html#msg38568None of these practices is designed to investigate, develop or improve technique. For these you need other sorts of practice. All of these speed practices assume that you have already mastered your piece. They are aimed at perfecting the piece. If you are still in the learning stage they are useless at best and nocive at worst.
Just like it is not about the number of hours one practices, it is not about the notches in the metronome.

I hope this helps.
Best wishes,
Bernhard.