Assuming your Time Machine volume is in an APFS container on the external SSD, create a new APFS volume in the same container. The new volume will share the available storage space.
Next, use Migration Assistant to install apps and system settings without user files on the internal drive.
Then, manually create user account with user folders on both the internal and external SSDs. Use Finder to copy folders from the Time Machine backup volume trying to balance the data between the internal and external storage. Files needing backup with Time Machine (in a new backup set) should, where possible, be placed on the internal drive.
If this works as intended, delete the old Time Machine APFS volume and create a new one as below using Terminal. Once created, add to the new volume to Time Machine (you should also consider using Time Machine options to exclude the external user folder).
diskutil apfs addvolume diskn APFSX "Time Machine-1" -quota nnng -role T -passphrase phrase -passphrasehint hint
(where diskn is the APFS container disk and nnn specifies the number of GB allocated to Time Machine; note that the passphrase and hint are only specified when encryption is required)
Hope this helps.

P.S. I thought it might be possible to use Migration Assistant to move user data piecemeal (e.g. separate user accounts) but this seems not to be possible in your case