Are "wonder" and "wander" etymologically related?

Especially in lyric-writing, where used more figuratively than literally, e.g. (mental) wandering and wondering, the two seem often interchangeable. And I can see wondering being conceived as an analogue of wandering (only, in one's mind). However from peering at their etymologies (see: wonder and wander), it appears this isn't the case—or have I simply not dug deep enough?

The two words have separate origins, although they may have crossed paths along the way.

Wonder comes from Old English wundrian, the verb form of wundor “marvelous thing, marvel, the object of astonishment,” from Proto-Germanic *wundran (origin unknown). In Middle English, the noun became associated with the emotion of wonder (late 1200s), and the verb had a transitive sense meaning “to inspire curiosity in.”

Wander comes from Old English wandrian “move about aimlessly, wander,” ultimately from Proto-Indo-European *wend- “to turn.” It's related to the verbs wind and wend. This word also became associate with the mind, emotions, affections, etc., in Middle English (c.1400).

Thus, wonder comes from a uniquely Germanic noun, and wander comes from an Indo-European verb, but they both became associated with the mind in Middle English. It's quite common for similar-sounding words to influence each other through confusion and wordplay, so there may be some convergence – you certainly aren't the first person to notice a metaphorical similarity between the two.