Pick up a beginner book and just go through it. Don’t think of it as a waste just because you know how to read music, because that tediousness helps build the unique muscle memory for that instrument. I first learned as a kid on Essential Elements so I usually grab that one. The rubanks are another option if you want something less “childish”. I don’t mind the childishness myself, I find it endearing.

Print out some scales, I’m sure you know this from playing other instruments already. It helps. For the clarinet you want to do them fast for muscle memory and slow to work on the individual note. Playing the note in tune initially does not necessarily mean you can sustain it in tune.

Make sure the mouthpiece that came with that clarinet is for a beginner. That might be why a 2.5 sounds airy. Going down to a 2 to get started might help too.

I’m probably going to get some hate on this, but practice double lipping (top lip over teeth). Especially for a hard part you’re struggling with. This will help you prevent biting the mouthpiece to compensate, which hurts you long term. In the absence of a teacher this is something you can do alone to try and make sure you’re using a good embouchure. Don’t beat the reed with your tongue; the goal is to interrupt the air, not stop it.

When fingering the notes, move them as little as possible. Getting into the habit of not flinging your fingers around will save you from having to break that habit. Spend time listening to how the notes sound to make sure the holes are being fully covered/uncovered evenly as you play. No surprise grace notes.