I don't think any of these services is "fully" free to use, by ideological standards; and I haven't reviewed any of their policies in detail to figure out which of the freely-given data and metadata is the cost of the freemium tier. Logs are definitely kept while the "remember context" setting is enabled, and I wouldn't be surprised if part of the agreement between services like these and the inference providers allows retention of partially blinded logs by the providers for improvement of their models.
Specifically regarding GPT4Telegrambot, all the heavier models are available only to subscribers; the free tier only gives "lite" models. The ones I used most in the way described above are GPT-4o mini and GPT-5 mini; there are also Gemini and DeepSeek models, although I've not played around with them much just because the OpenAI models were the default and honestly I was more interested with getting good enough results than surveying the entire market.
GPT4Telegrambot, all the heavier models are available only to subscribers; the free tier only gives "lite" models. The ones I used most in the way described above are GPT-4o mini and GPT-5 mini; there are also Gemini and DeepSeek models, although I've not played around with them much just because the OpenAI models were the default and honestly I was more interested with getting good enough results than surveying the entire market.