Start Edition can only open/save certain file formats:
http://www.archicadwiki.com/StartEdition
According to that page, you can open any earlier SE edition format, and the professional (full license) version of AC can open any earlier SE format.
The file compatibility DOES make it easy for a firm to start out with Start Edition (the reason this edition exists)... and then later migrate to a full license, knowing that the work they performed in SE will migrate to a full license PLN file.
SE is NOT intended for the purpose you have suggested: being able to open normal files from any professional version. It is intended for people just starting out with ArchiCAD... or those who do not need to move old projects forward, but are starting only fresh projects.
Many (most?) resellers will give you a credit for the amount you paid for SE towards the purchase of a full license if that is what you require.
One of the forum moderators
AC 28 USA and earlier • macOS Sonoma 14.7.1, MacBook Pro M2 Max 12CPU/30GPU cores, 32GB