How to split video signal via HDMI?

Question

Video

Foreword:
Given: video source - laptop with HDMI output, three projectors, Chinese HDMI splitters, HDMI cables 15+ meters, video signal - Power Point presentation and video.
To hold events, it is necessary to broadcast the image to three sources (three projectors). The scheme is as follows: computer - HDMI cable 3 meters - HDMI splitter - from it one cable 15 m to the first projector, the second cable to the second (!) Splitter, from which there are two more 15 m cables for 2 projectors.
Such a system works extremely inefficiently: it works every other time, the picture disappears, in order to set it up you need a bunch of dances with a tambourine. Splitters, cables, chargers for splitters, laptops, projectors have been changed - it always works crookedly.
Reflections on this: I always thought that the twisted-pair solution was a self-made collective farm. I recently realized that I was wrong. A 15+ meter HDMI cable is extremely inefficient, and the twisted-pair solution is offered by HDMI itself.
Bottom line : if I understand correctly, then correctly (assuming one computer, one projector) the chain should look like this: computer - hdmi cable + -1 meter - hdmi-lan converter - twisted pair cat 6e 30 m - hdmi-lan converter - hdmi cable +-1 meter - projector.
Questions:
1. Do I understand everything correctly?
2. Where to insert the splitter at this stage? Which is better to choose?
3. Which converter should I use?
4. How to optimize the circuit?
5. How to make everything work?
The budget, as usual, is limited.
I would like to spend up to 200 ye on cables, splitters, converters.
Many thanks in advance for your replies!

Answer 1

Option 1 Laptop
-> HDMI cable -> HDMI-to-LAN splitter transmitter for the desired number of recipients (usal, which transmits a signal over 2 twisted-pair cables 5e over a distance of up to 30 meters! ) -> 2 cables twisted pair cable 5e (length UP TO 30m) -> splitter receiver -> HDMI cable -> recipient (TV set, projector)
Option 2 , as suggested above:
Laptop -> HDMI cable -> projector1 -> HDMI cable -> projector2 -> HDMI cable -> projector3 - BUT, I had an old projector, the projector only had a VGA output, so it's not a fact that this option is viable :(
PS: you probably won't fit into the budget with option 1