Welcome to the MongoDB Community Forums @Jakub_Sygnowski !
As @tapiocaPENGUIN noted, M0 and other Atlas shared clusters (M2, M5) currently receive automatic server version upgrades. Per the email communication you received, the major version upgrade to MongoDB 5.0 will happen this month across the global fleet of shared tier servers.
MongoDB driver versions are compatible with a range of server versions, so if you upgrade to the latest driver for full MongoDB 5.0 feature support, this driver should also provide support for previous non-EOL server releases (at least as far back as MongoDB 4.0 at the moment).
Upgrading to the latest driver version is highly recommended for full compatibility, but is not a strict requirement. If your application is using a slightly older driver (for example, one including full 4.4 support) I expect you are unlikely to encounter any issues aside from lack of support for new server features. If you are using a much older driver (for example, one targeting 4.0 support) you are exposed to a much broader range of server changes. MongoDB 5.0 also introduced a new Stable API (originally called the Versioned API) that provides a guarantee of future server compatibility so you can Upgrade Fearlessly if you adopt it.
The MongoDB server release notes include Compatibility Changes in MongoDB 5.0 to be aware of. Many of those are specific to server configuration and would not apply to the Atlas shared tier.
For related discussion, please see Automatic upgrade to MongoDB 5.0 - #4 by Jason_Tran.
Regards,
Stennie