Option to intentionally delay levelling-up to avoid getting overwhelmed

I believe there is a script: [Userscript] Lesson Lock See if you can set it up the way you want!

And of course, as others have mentioned, if you’re not too worried about leveling up quickly, you can use [Userscript] WaniKani Lesson Filter to spread out your kanji lessons. As long as you save 4 kanji in your lesson box, you won’t be able to level up. As soon as you have 3 or fewer kanji left in your lesson box, you will be on track to level up within 3 days at the soonest.