My experience with the tonewood aspect of fretboards is based on 45+ years of gigging on the dark side as a guitarist using Fender Stratocasters (among other guitars). IME, there's been a tonal difference between every rosewood and maple fretboard Strat I've owned, especially played at clean-to-low-gain settings.
IME this has been consistent with basses.
I was blessed with the chance to meet and hang with Stevie Ray Vaughan in 1980. One of the things we discussed was the maple/rosewood thing on fretboards since I just couldn't make maple board strats work for me. His opinion was maple provided more bounce and brilliance; Rosewood, a warmer, darker, more grainy tone.
I still agree with this. Sure, the strings are more in contact with the frets than the board. There's indirect contact though; The strings resonate through the entire bass, bridge, nut, body wood, neck wood, and especially fretboard wood since that's what anchors the frets.
A couple examples from Stevie:
"Lenny" from his debut album, recorded with his maple fretboard Strat by the same name. Strong Curtis Mayfield influence on this one, BTW - Curtis' main guitar was his white maple-fretboard Strat.
"Texas Flood" from the same album, recorded with his #1 rosewood board Strat. A lot more heft and warmth.
Back to basses: I prefer the maple board on my Precision because of its quicker note attack over every rosewood board P I've played; Still, I love the warmth of the rosewood-board P's, and find them more visually appealing, just digging the maple fretboard thing on mine.
OTOH, I love the rosewood fretboard on my 2010 Road Worn Jazz, so there's that.
IME it makes even more difference with fretless because of direct vs indirect string contact. Personally, I prefer the fretless tone of tight and smooth fretboards. My cheap Squier CV 60's fretless came with an unfinished Indian Laurel board, which didn't much sound like the fretless tone in my head.
I "ebonized" it with multiple coats of scratch resistant gloss polyurethane (after dark staining it). Night and day tonal difference, plus the stain almost covered up those annoying lines.