Hello!
Sorry, our testing system is Mint 21.1 Xfce edition and, provided that you install bash, everything runs perfectly, including traffic splitting. We will test on Mint 21.3 and 22.1 in the next days and let you know. The log shows multiple critical problems that are not currently reproducible. We will update this thread in due time.
As far as it pertains to ufw, Bluetit does not disable anything, but Network Lock operates at nftables level in your system through the userspace utility nft, because Bluetit detects that both nftables and nft are working in your system. However, ufw is an iptables frontend, so it can not interact directly with nftables, it must do it through legacy translations. This hybridization is deprecated because it may cause very many problems (Bluetit tries to warn you with "WARNING: ufw is running on this system and may interfere with network filter and lock" as you may have seen).
ufw does not support nftables, which is the new network filtering subsystem of your distribution Linux kernel.
iptables compatibility is maintained through a complex set of translations. If you operate simultaneously with nft and ufw, bad things may (will) happen. When Bluetit restores the previous rules, it does so via nft. If ufw gets disabled at this stage, it's not Bluetit that disables it directly.
The above firewall problems are not user's direct responsibility, instead they look like the outcome of a suffering and maybe not well planned migration from iptables to nftables on Ubuntu and derivatives. Please note that in Mint 21.3, ufw is disabled by default, thus resolving the problem at its root.
Solution: consider to clean up the system to stay entirely on translations or entirely on nftables. If you want to go with nftables, just disable and/or uninstall ufw.
If you prefer to keep ufw then renounce to nft and rely exclusively on translations, and force Bluetit to go back to iptables translation. To do so, just change the networklockpersist setting into iptables (from the default automatic choice).
Kind regards