Is there any MacBook-supported filesystem that will not do a scan every time its underlying external HDD gets unplugged without eject?
When a file system is improperly disconnected, the is a likelihood that there are partially completed write operations. In the simplest cases this might just lead to the corruption of a single file.  But if the file system was in the middle of making a directory/folder change this would lead to the whole folder being corrupt.  In the worst case, it could make the file system unusable.
So it is a good thing that macOS makes sure that the file system on any improperly ejected file system is intact and in a consistent state.  You would be very unhappy if there were any problems with the file system that led to a loss of data.
For simple file systems the checking needs to be of the whole file system.  And that is slow, as you know!  But, worse, there is a good chance that the disk may become unusable if it was in the middle of multiple write operations.
More modern file systems keep a journal of changes so that after an improper ejection, the file system can be set back to a consistent state - undoing any partially completed operations. As well as being more sure, recovery is much quicker than for older file systems. This technology (and its theoretical basis) was developed for databases (in the 1970 and 80s) and later extended to whole file systems.
Both the HFS+ and APFS file systems are journaled and are the usual file systems for disks used only on Apple systems.  Windows NTFS is also journaled, but not so easily used with macOS.
So the short answer is to use APFS or HFS+.  Recovery will not be instantaneous (and macOS may complain about the mistreatment of the disk), but it will be quicker and more certain than when using exFAT. For better recovery use APFS rather than HFS+.
But, be aware that accidentally unplugging a disk (particularly an HDD) can lead to physical problems on the disk drive. So don't make a practice of improper ejection if you value your data!