@hobbya was able to locate the datasheet of the ETA at LCSC
But you are still right in the end, because I was refering to the different formula to calculate the charging current for the ETA, but just simply overlooked the square in the formula yesterday. Without the square it would be around 270 mA (incorrect) instead of now again ~360 mA.
In the datasheets of the XC6802 and the ETA4054 is not exactly specified what happens, when there is simply no battery connected without a proper shut-down. But I came to the same conclusion that it will probably behave as in Standby Mode.
It will then consume around the values you provided (60 to 100(max) uA, maybe even 200 uA regarding the above note).
This all would kind of confirm (except the blinking of the LED) my initial question and makes the XIAO only usefull for low(er) power applications when powered over the battery only.