Save online updates the wrong score when switching tabs during upload

Yes, I think to have observed this too, even with 2.1 or maybe even earlier.
The 'source' tag in the 2nd score is replaced/updated with the one from the 1st (the "Save online"ed one), and then on "Save online"ing that 2nd it updates/overwrites the 1st.
Pretty bad thing. Mind to enter that into the issue tracker?

I experienced the exact same issue. Jojo-Schmitz - I discovered your workaround on
https://musescore.org/en/node/273844
which was for a slightly different scenario, but same workaround and included it on the issue tracker:

1) Get the URL of the score that should be uploaded to
2) File -> Score Properties -> source (paste the URL of the score and save)

I logged an issue at
https://musescore.org/en/node/273858
Please confirm that the sequence is correct w.r.t. which overwrites which one's URL.

This Score Properties source field is extremely useful. I have had a .mscz file go out of sync with its online score (same scenario as https://musescore.org/en/node/273844 ; having to upload using the browser-based update score feature) and this re-establishes the link. I thinks a How To or other page would be very beneficial.