I think that depends a lot on the particular product, but I would say that it ought to feel dry and not sticky or not soft before recoating. I make my own using a 50-50 mixture of Varathane polyurethane and naphtha. That formula was made famous by Jim Kull, a furniture restorer, on the Wood Online forum about 20 years ago. I prefer it over any commercial WOP. If you want slower drying then use mineral spirits in place of naphtha. I think that any brand of poly would work, but I got stuck on Varathane many years ago. Varathane is now a part of Rustoleum, but it seems to still be the same formula. Also, Varathane contains both naphtha and mineral spirits so both are compatible as thinners.
In the north central Texas climate, I can usually apply two coats per day and sometimes three, but I avoid rushing things. If I had used mineral spirits then one coat per day is the max. Don't do anything to the finish between coats because that will only make a mess that can't be easily fixed. I don't see a need to polish the final coat, but if you want to soften the sheen then you could use pumice or rottenstone. Rottenstone and Tripoli are very similar so no need to have both except that rottenstone comes as a loose powder which makes it much easier to do French polishing. Tripoli is often mixed with a hard wax and molded into cakes ... not very convenient for this purpose, but still can be used if you break it into a fine powder
If you do anything to the finish , I suggest waiting at least a couple weeks because cross linking typically takes that long or longer despite the surface appearing to be fully cured.
If you are having problems, it might be because poly seems to be especially fussy about surface preparation. The surface needs to be especially smooth and clean because the poly seems to magnify even the slightest imperfections like scratches, raised fibers, and dust. Tiny sanding scratches more than anything else love to show up in all their glory when a glossy finish is applied. I've found that it helps a lot to raise the grain with alcohol and then sand down the fuzz after the wood dries. Otherwise, the grain may fuzz up when the first coat of WOP is applied. Allow plenty of time for the alcohol and water to evaporate before applying the first coat.
I think that the best applicator for WOP is an old T-shirt rag. I apply WOP in a thin film, but wet enough to leave a gloss. Don't try to rush the process by applying thicker coats. That will just slow things down as it takes longer for each layer to dry sufficiently before the next application. When applying, only wipe the poly once and avoid repeated strokes in an attempt to "improve" the appearance because it won't ... that just leads to bubbles and streaks. Imperfections, dust nibs, and bugs can be dealt with later. Just one swipe of WOP then move to the next area. The total number of coats depends on the wood and what you want. Because the Jim Kull formula results in a thinner varnish than most commercial mixtures, you need a minimum of three coats and up to six coats for some wood.
I've only used this on furniture, because I prefer other finishes on woodturnings. The reason is just my opinion that as a fairly hard finish, poly might be more difficult to fix problems and still wind up with a nice looking finish, but I am just speculating here. A round piece of wood where you see end grain and side grain in close proximity could possibly present a challenge in getting a finish to look consistent in both uniformness of color and consistent surface appearance with WOP. Sometimes a shellac seal coat (one pound cut dewaxed super blonde shellac) helps and sometimes ring porous woods like red oak and ash seem like they can never be satisfactorily leveled. It's probably not necessary, but I prefer mixing my own shellac flakes with alcohol and filtering it so that I know what I have is fresh and dewaxed.
Cross linking in poly takes a very long time despite the surface feeling dry. For that reason, it is not necessary to scuff the surface to get adhesion between coats if they are applied within twelve hours or so ... maybe even 24 hours. If a coat were applied several weeks later there might be justification for sanding before applying the next coat, but I seriously doubt it. When talking about WOP the surface might appear glass smooth and impervious, but under magnification it is surprisingly porous ... it's just that at the limit of resolution of our eyes (approximately one milliradian), even at the closest viewing distance we are able to focus, we can't see the surface roughness. I did a mythbuster test once to see if polyurethane varnish would adhere to glass. I found that after leaving it alone for several months, it was very difficult to scrape off the glass using a razor blade. While my test isn't proof of longevity or anything, I feel confident in not needing to sand between coats.