Temperature controllers with wifi: autonomous operation and recommended models up to 500zł

Hello
I'm thinking of replacing the regulator as in the topic with something with wifi. On Ali I see a lot of this at prices circa 100-200zł. E.g.:
https://pl.aliexpress.com/item/1005003324986217.html
or e.g.
https://pl.aliexpress.com/item/1005004786531681.html
I like the latter (in the image )

Question: do these types of controllers have their own schedule memory? Can they work autonomously in case of lack/loss of internet access?
And maybe some other model worth recommending and possibly more money, say up to circa 500zł ?

Greetings.

The savings from installing such a regulator are small, not to say non-existent, and the cost is significant. And you know what the best thing about it? If the battery is weak, just that of poorer quality, it will only increase the flow because it goes lighter because the spring of the thermoregulator is loosened and if the heater goes full for a month, you will have eyes like 5 zlotys when you get the heat/energy bill.

Buy yourself a Roomba WiFi, equally useless but at least it is safe for your finances.

@Stanley_P, I use a THERMOVAL TVT 31. Before I bought it, I did some research to find out if it could be connected to HomeAssistant. The answer: there is a suitable integration (hass-floureon) that allows you to control it via LAN. I cut the controller off from the internet on the router and control it exclusively via HA, and I am satisfied with the result
What about the schedule memory, I won't 100% confirm to you because I don't use this functionality (HA took it over), but it seems to me that it is independent of internet access because everything can be clicked manually from the physical panel, so there is no need to install the manufacturer's app (and therefore connect the controller to the network).

From what I gather, the newer regulators of this company are probably already based on the Tuya cloud, so cutting them off from the internet can be troublesome (as it is with Tuya).... I would, therefore, rather recommend the older models.