LogFAQs > #962399134

That's consistent with the way the PC works in other games (or at least SwSh). It's just more annoying because you're catching more, and no matter what the new Pokemon always start from the beginning instead of whatever last box you were using.

Midway through the Mirelands, I figured the best way to tackle the pastures is to leave the first few empty for new catches to pile up in, and to start organizing my living dex with pasture 4.