@cwerty
It's far more likely your eTrex is malfunctioning because of firmware or flash damage problems. I very much doubt that changing/adding files will help you to recover it.

I have many questions:

Is your device a "standard" etrex 32x or is it marked as eTrex 32x 2022 Redesign on the ID label?

How did you flash the modified 4333 firmware? i.e. Did you use an RGN file in Updater.exe or individual BIN files using Update.txt in a media card? (a device with a different HWID won't accept a GCD flash with a mis-matched HWID).

Why did you know to try using 4333 fw when it was identifying as 3445? i.e. Did you or someone else change its HWID or "cross-flash" firmware previously?

So, if you know, please say what is the complete modification history of this device BEFORE you obtained it. Without knowing that, any further manipulation of fw might make things worse and even hard-brick it.