Thanks for the extra info. A photo of the front and back would be nice.
So basically anything that can switch on 240volts at about two amps when the temperature drops below setpoint will do the job.
Everything else is decorative.
Your gas combi boiler may have a diagram inside the door and specifications on a label that may also assist in device selection, having jumpers for different kinds of thermostat technology. Ultimately, that is the specifications you need to comply with. Sadly that information is not here (yet). The installers guide for most can prove to be most instructive.
Short term maintenance suggestion while you continue your investigations: Check your existing thermostat for cobwebs, spider egg nests, dust and fluff buildup, or other obstructions internally that may be interrupting airflow past the sensor (power off of course). Clean the contacts gently with a cotton bud dipped in hand sanitiser/alcohol won’t hurt either. Post a photo if you want comment on their condition.
Hysteresis is a normal expectation of heating and cooling, the mass of air and water taking time to heat and cool - not instantaneous. There are climate integrations that can account for this, switching on and off as the threshold is approached, some in hardware, and others in software. Common in HomeAssistant climate integrations too.
Consider a ESP32 board with a relay (usually rated 250volts at 10amps - more than adequate) and a display and some buttons and a fancy case and you could roll your own, or go with one of the vendor supplied ones that is cloud connected but can be customised to free it from the cloud by custom firmware from ESPHome or Tasmota or the suchlike. There are many designs, and even the ESPHome website at Thermostat Climate Controller - ESPHome - Smart Home Made Simple and Bang Bang Climate Controller - ESPHome - Smart Home Made Simple will give you some insight into issues to consider.
Where you place your temperature sensors (you can have more than one) is important. They are traditionally part of the temperature control case, but do not need to be. Keep them away from doorways and other places where they will give false readings. You can place your control and display in one place, the temperature sensors in another, and your relay portion near the gas combi boiler for maximum flexibility, convenience, and signal strength if you are going wireless (WiFi/ZigBee/Matter-Thread/BlueTooth, etc) or hardwired like RS485/ModBus, existing three wire mains rated cable etc.
You might want to call a HVAC installer to give you a free quote on an upgrade and pick their brains while they are at your home on what options to take. An old and experienced one will probably give you wise suggestions. Why stop at one - after a few you will get the common thread of what you need, rather than what is cheapest and nasty, or makes them the most profit.
The WAF factor is vital. Anything complicated and you sleep on the lounge tonight! Any knobs that invite random fiddling by passerby visitors and children are out. You shouldn’t need to have a padlock on the box over the controls, but consider child-proofing it by having to enter a code to enable any long term configuration changes. Even a separate BOOST button may be a viable option.
Everybody will jump in with their own suggestions on what to buy, but at the end of the day, your gas combi boiler is just waiting for 240volts to come down the wires to start it working, and when it disappears, to stop working - no more, no less. You can verify that by jumpering the control to live wires at the back of the thermostat and watch the boiler come on.
Feedback on what approach you take would be appreciated. Any further questions welcome.