Let's Control It

Can somebody suggest where to find suitable pulse sensor for watermeter from appended picture.

Some of those water meters have a magnet in the dial that rotates at the highest frequency.
You could then use a Hall-effect sensor to detect pulses.
A glass reed switch is then not the best suitable.
Some of these Hall-effect sensor boards have a LED, so it can then be moved over the glass to locate the magnet's position.
Then you need to use some water to see if you found the right spot for pulse counting.

Some Hall-effect sensor boards also have a trimmer to set the sensitivity.

I prefer reedrelay because reading of pulses will be on location without power supply and ESP will run on battery with longest possible deepsleep period.

But then you will miss pulses, if the ESP is in deep sleep.

And a hall effect sensor can also be seen as functionally similar to a reed switch.

Only deepsleep is't a solution for batteries. I use attiny for counting and ESP-01 for trasmiting (MQTT or HTTP): https://www.hackster.io/dontsovcmc/waterius-4bfaba