[JonPR]

You're in the reverse position to many beginners - and I don't mean because of your extensive experience.

The typical beginner (these days) knows plenty of scales, but doesn't know chords well enough, or has no idea how to use scales musically.

You're in the (advantageous) position of knowing plenty of chords - I imagine you see your fretboard in terms of chord shapes. Your problem is (in a sense) how to break out of those shapes, open out into scales.

What kinds of things do you do when you play a fingerpicking break? Do you stick solidly to each chord shape? Or do you embellish them with an extra note or two here and there? Maybe a hammer-on or pull-off? If so, you're on your way; you're already using something of the strategy I'm outlining below.

What I suggest is you take the I-IV-V chords of any key, using shapes you know in the same neck position (any position). I.e., you can play all the chords within a 3 or 4 fret "box". The notes you're holding down - adding all 3 shapes together - is your scale; it should be a near complete scale, running over two octaves (if you're using all 6 strings). Whichever chord you're on, the notes in the other chords are your additional passing notes.
I.e., there is no magic to scales, nothing you don't already know. Just as chords come from a scale, so the scale comes from the chords. No new knowledge to acquire!

It's probably a good idea to use a pick, to get out of the fingerpicking habit. Just pick your way in and out of the chords. The left hand will obviously not sit on each chord shape in full (you need to release it from that task), but you still "see" the shapes there, so you can use chord tones as starting notes and target notes.

That's a fairly "vanilla" approach, because (from I-IV-V chords) you're using the diatonic scale of the key. No chromatics. If you want a bluesier or jazzier sound, that's when you call in the chromatics. Start by using notes a half-step below any chord tone: slide up to the chord tone, or hammer-on. You can really use any note at all when soloing (all 12 are up for grabs) but it's the chords that make sense of it all, where the phrases all resolve.
That's where your own real advantage lies: your chord knowledge. You will never get lost because you will know what chord you're on at all times.