Well, I made a small investigation so answering myself.
iBasso, even though they didn't answer me yet, seems
well aware of the issue for a long time ever since 2019 and DC01.
Workarounds are to "charge" the dongle a few seconds first on another device or powerbank (works everytime, it's like giving a boost to start your car with another one when your battery is empty hehe) or connect the dongle to an usb-c type hub then plug the hub to the phone, or plug the dac first and then restart the phone to get it recognised everytime you want to use it.
Very practical and straightfoward

Haven't seen anything like that yet. I don't understand why it is working when plugged to an usb-c hub and not directly, makes no sense to me. It's like the usb port going to sleep mode if inactive and doesn't want to be woken up by a DC03 pro. Why would it be specific to iBasso though, as other dongles, even more powerful ones, don't have the issue. Maybe it could be easily resolved by a firmware update. This phone series won't get anymore android, samsung or even security updates anymore so no hope from samsung side of things. iBasso mentions it as a Samsung related problem (often S10, S20, S21, Note 9, Note 10 it seems on forums, maybe others), that's a lot of potentialy concerned users..
Would you keep a dongle, as good as it sounds, with this kind of hassle to make it work?
Is there some samsung galaxy users with Tanchjim Space here? Might be the next try.. or might end with a DAP to be safe.
(SXFI Amp compatibily with S10 is also very bad by the way, clicking / popping noise, no possible USB exclusive mode etc. Don't know if that changed since its X1 replacement)
EDIT : easiest and portable solution seems to be using an OTG USB-C to A adapter >> USB-A to USB-C (plug this combo first seems to wake up the port and phone) then "charge" the dongle and then plug it back normally within the next 10 seconds.