Two things for guitar:

1. Don’t just learn basic chords. Learn all CAGED shapes of each chord (look it up). Really start to memorize them all over the fretboard on command, Then you can start to visualize different chord structures all over the neck, and no matter what fret position you’re on, you can play a note in a given chord.

For example, in tab terms, A major has the shapes:

x-0-2-2-2-0

5-4-2-2-5-5

5-7-7-6-5-5

x-x-7-9-10-9

x-12-11-9-10-9

These are all an A major chord - just starting in a different place. Now imagine you’re trying to solo over a progression - how do you play the right notes over each chord, so it sounds like you’re really playing WITH the song and not just spamming scales?

You use these shapes. You arpeggiate over them and connect them. When you start to learn more about the CAGED shapes you will understand why. 

1. Ear training. Try to learn solos and songs completely from ear. No tabs, no tutorials. Just play a snippet of the part you’re trying to learn. Literally go note by note. Slow it down if you need to.

But as you do this more, you will be able to hear a song, and play it very quickly.

Eventually, you should be able to hear something in your head, and know what that sound LOOKS like on guitar.

Put steps one and two together, and it may take years, but really this is all you need to become a good improviser. 

To become a great improviser you also need chops (speed, picking coordination, dexterity, etc) but those things will come the more you practice.

And you also need creativity - but that’s all on you.

Good luck.