You can use RSC, using which you can request team owners to consent for a bot to receive user messages across standard channels in a team without being @mentioned.
Please check this doc for more details - https://learn.microsoft.com/en-us/microsoftteams/platform/bots/how-to/conversations/channel-messages-with-rsc?tabs=dotnet, https://github.com/OfficeDev/Microsoft-Teams-Samples/tree/main/samples/bot-receive-channel-messages-withRSC
Please note that this feature is currently available in Public Developer Preview only.