Any new sd card requires formatting directly in the phone preferable as external storage for easier data exchange but with the sacrifice of encryption.
Is the sd card listed among the FP2 compatible types as listed here?
Running out of storage always is a crucial situation even these days. It´s like being blocked in a parking lot without any space to maneuver.
Swapping the sd card alone if your internal storage is full as well won’t help much as most file transactions are on the internal storage. Your OS (+the apps) -> the phone needs room to operate and perform. If all space is used up things will be blocked and maybe cause unpredictable errors or behavior ->read only permission.
Most important now is to free enough space to at least get the OS +apps running.
Since the option of using any computer to move data to is not available atm you have to find an alternative way to achieve this.
With data I mean personal things such as music, pictures, videos which you have direct access to.
Usually starting with smaller files (file size) get you going.
To stop further data input (via messenger etc.) any network/mobile connection should be disabled to keep auto-synching/updating apps from gathering more data.
One reboot should then be performed.
If you don’t wan’t to delete personal data, you could delete apps or look out for a trusty person to maybe temporary store some of your data on their phone using a bluetooth connection. Activating this should require little to none further space. Actually data have to be moved not simply copied.
If you have (thrust) the google drive cloud storage would do too (other apps will also keep on using the connectivity probably causing error messages). But if not active it may not work getting the google drive activated if there is no further free storage in your phone left.
You have to free enough space to have the phone in an operational state for:
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read + write permissions again
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formatting your new sd card
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delete or move some apps/personal data to the sd card
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recover your temporarily stored data via bluetooth again (or from the google drive)
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eventually activate network connectivity again