Generally under linux this is not a problem, multiple applications can access the same file without issue. It is an issue under windows, but restic integrates VSS support to mitigate that.
The primary benefit snapshots provide under linux is point-in-time consistency of every file in the backup, which may, or may not, be important depending on how busy the system is in terms of writes, and how big the backup dataset is.
I can’t speak much to the LVM setup, but you appear to understand the btrfs snapshot setup well enough.
It might be simplest to just treat or think of btrfs subvolumes like they’re individual partitions, because in terms of snapshots they behave a lot like they are.
Which one you should use depends on how your machine is configured though surely? If you have a btrfs setup, you should use that. If you have ext4 or xfs, LVM is the only option.
If you want my advice? Keep it simple. If and when the unthinkable happens and you need to restore from backup, you want the process to be as quick and painless as possible.
i.e. use snapshots only if you actually need them, and take a full system backup only if you actually need to. Backups of user data are much simpler to work with.
Regarding btrfs snapshots/full system backups, you may find the discussion in this thread interesting/useful:
Whatever approach you decide on, please make sure you thoroughly test the restore process you come up with. Backups are worthless if they cannot be restored, and a full system restore is always going to be significantly more complex than a regular “user data” restore, so you need to be sure it works before you have to rely on it! 