I started out with a Zoom B1-X with the expression pedal and the whole works. Loved it and used it a lot to explore different effects. Then I sold it to another BassBuzzer and got the Zoom B3n and another expression pedal. Again, I used it to explore the different effects and combinations of effects. In the case of both Zooms, I never used the looper, drum beats, or the tuner (I have a DAI, Reaper, tuner, and drum machine for those functions).
After awhile, I got tired of the multi-effects and decided to get a pedal board and start adding individual pedals (for the reasons you cited in your post).
I brought my Zoom B3n into my local music shop and talked to my bass guy about trading it for some pedals. He took it in and gave me a credit for some pedals. While I was picking out my pedals, he chuckled and told me that they get a lot of guitar and bass players who start out with multi-effects devices and grow out of them, eventually switching to individual pedals just as I am doing.
So, with that story told, your answer is right there between the lines. Start out with multi-effects and get an idea of what each effect does to your tone, then decide to either stay with the multi box or go with pedals and pedal board. Some people here have both the multi-effects box and a pedal board, but to me, that would take up too much real estate on my floor.
P.S. I recommend buying a used multi-effects box on Reverb. That way, if you flip it later on and buy pedals you won’t lose as much money.