How can I fit synchronised locks on two bathroom doors for a few hundred zlotys, with an emergency r

Hello.
I have a fairly long and narrow bathroom with doors at opposite ends. I want my guests to feel comfortable, whether they’re using the toilet or having a shower. Are there any sensible solutions that don’t cost a small fortune, which would allow the locks on both doors to be locked and unlocked simultaneously? I’ve come across some ‘miracle locks’ costing 3–4 thousand. I’ve also read about Zigbee or Z-Wave smart systems, but availability in Poland is very limited.
Hence my question: has anyone here used such a solution and can recommend one? The cost should be no more than a few hundred. As long as it’s reliable, has a mechanical unlocking option (in case of a power cut) and, ideally, doesn’t need to be plugged in (though that can be done if you’re determined).
Thanks in advance for your help,
J

I’ve seen this sort of layout before. Two living quarters shared a bathroom. The bolts were fitted in the door frame and were connected to each other in such a way that they could be locked and unlocked from either side; if I’ve understood it correctly, a rail ran the entire length of the bathroom ceiling, with the bolts mounted on it.

In your case, the only sensible solution is two electromagnets that can remain engaged for as long as required. When switched on, the electromagnets lock the doors. In the bathroom, next to the door, there are two staircase switches powering these electromagnets. Each switch independently turns the electromagnets on and off. A power cut causes the door to unlock.

Such electromagnets are relatively inexpensive and widely used.