Yeast management has the right way and ... other ways!
Ideally you crop yeast at a point around high krausen/after 24 hours/at 50% of fermentation (experience tends to lead here) off of something which is certainly less than 6% and repitch as soon as possible. Before use assess viability and perform a cell count to determine a constant pitch rate. It should be chilled to compact, the balm ale almost completely poured off, kept chilled and used within a few days. Viability loss on storage can be decreased by keeping it under a layer of distilled water, but you don't really want to keep it longer than a week. With a good flocculant strain cell density can be as high as 3*10^9 per ml.
With top cropping and open vessels this is quite easy ... with a bottom cropping strain you'd dump loose material from the bottom and collect comparatively quite a lot or you'd transfer it straight over to fresh wort staggering your brews. Chilling helps to compact it down, but to store a bottom cropping strain in the required amounts is best with something like a yeast brink. You end up needing more slurry because it has a lower cell density. Standard bottom cropping is usually lager, the point to crop is much later, like a week in. Some kviek is bottom cropped, I've no experience of it except at home where I store and prop off starters each time, pioneers are on their own in a commercial brewery!
Sealed vessels and top cropping introduce other challenges. Tend to take yeast a little later in the fermentation when bottom cropping a top cropping strain, it is a bit of a compromise, some strains flocc out lovely, some need a gentle chill, others are awful and almost a waste of time to crop, again calling for a brink, cropping little and often. The later you leave it the more yeast is dead, but the more yeast has dropped. Tank time needs to be accommodated for. It becomes a game of how long can I leave this because it is eating into my dry hop time and do I have the time to slightly chill it to crash the yeast and extend the dry hopping time to accommodate for the lower temperature. It influences the decision on what strains are desirable to use. It can be enough to make you use fresh yeast all the time, but the additional cost, especially externally propagated wet can limit creative options when brewing.
Brewing is often about finding budget solutions though, so we'll do stuff like brew a weaker beer where the dry hop doesn't matter so much which we can crop to death alongside a stronger beer with the same yeast which is all about the dry hop, contact time, settlement and running off. The weaker brew allows us to keep the culture going while we've no intention of cropping the bigger beer and will proceed to dry hop much sooner. Even better if I can cost the yeast into a complimentary brew and then use the now 'free' yeast in another beer which now has a bigger budget for ingredients!
When reusing it over successive generations your aeration and/or oxygenation must be on point to sustain a constant heath and performance of the culture. After a while genetic drift (debatable, impact is strain dependent) can introduce undesirable characteristics and you should renew the culture. At any point, but also after a while you can pick up a few unwanted organisms which over successive generations reach a level where they introduce undesirable characteristics and again, call for renewal. In the meantime acid washing can extend the time on the second problem. House cultures can have an acceptable level of contamination as part of the charm because it never shows up under typical time frames.
In reality though you can do almost anything depending on your spirit of adventure and aversion to risk! What would I do in your shoes? I tend to build a starter for all the yeast I use at home. I reserve typically 2 vials of from the starter and use one to build the next. I'll typically reserve 2 vials of this one and I'll work through them in sequence. This way I've got a back up and I'm limiting genetic drift. They keep pretty well in the fridge, I've not had a failure to reanimate yet, but I tend to keep them no longer than 6 months. I also weigh if it is worth keeping a culture or if an older culture is worth using when presented with other options. I have access to quite a few yeasts via work and if I don't want to use any of the 3-4 strains on the go there then I'll prop some. I've also constant access to wort which helps.
