I took time again to test.
To resume: I only want to put Logic in record/pause mode and then when I start an external sequencer I want Logic to start recording, so all is in sync.
No matter what I do, no matter what setting, it does not work with the Beatstep Pro (BSP).
As mentionned earlier, as I know it always used to work fine (I insist), I decided to try with different MIDI controllers/sequencer. I tested with the Keystep Pro (KSP) and it worked right away (!!!). No need to change any setting, apply any key. It just works.
I put logic in record/pause mode, I press play on the KSP and logic starts recording.
If I wanted to record also at the same time on the KSP, I'd simply put Logic in pause mode and then click record on the KSP (or the BSP).
I tried with Keystep and it did not work.
As it just worked on the Keytep Pro which is connected to HST3 port on the Mio XL (USB port 3) and it does not with the controllers connected to the other USB host ports on the Mio XL, I checked the settings in Auracle (Mio XL admin so to say). The only difference is I have DIN12 not active on HST3. DIN12 is the MIDI port going to the Pulse+ synth (which plays no role in the game).
Abs. no clue why it is interfering***, but if I deactivate this DIN12 port, then the issue is gone. I can start recording from any ext. sequencer!
***and not asking here, as too many factors play a role in the studio. What I'll do is check the MIDI settings on the Pulse+.
This was a long journey!