This app was mentioned in 7 comments, with an average of 1.57 upvotes
You can get Solid explorer which gives you a Save to option in share using which you can save it in the folder you like and it would appear in the gallery.
Edit: found two other simpler options
Hi, my phone's power button is not working correctly to. I use this app for saving images. https://play.google.com/store/apps/details?id=com.sapps.savetodrive
Press home > Share screenshot > Select "Save To Phone" > Choose directory > Click Select and It is saved!
Or if your phone is rooted you can use tasker. Create task. Add Code > Run Shell action. Write command "input keyevent 120" and check "Use Root". Now you have options. 1. Download QuickTask plugin. And create Screenshot tile. And create tasker event. (Disable tasker root grant notifications in your root manager like magisk, supersu etc. Because It can be seen sometimes in screenshot and It looks bad. 2. Custom Navigation Bar: I was using double tap future but it is not working anymore, I hope developer fix this.
I've used this app whenever apps didn't have a 'save to gallery' option. https://play.google.com/store/apps/details?id=com.sapps.savetodrive
This app should do exactly what you want:
https://play.google.com/store/apps/details?id=com.sapps.savetodrive
It adds "Save to phone" as a share target.
You can try Save To Phone app.
The one I'm using is Save to phone:
https://play.google.com/store/apps/details?id=com.sapps.savetodrive
Here's the right one https://play.google.com/store/apps/details?id=com.sapps.savetodrive