As of 18 months ago, both Mattermost and Rocket.Chat, the other popular self-hostable alternatives to Slack, required a paid plan for mobile push notifications at the time we started charging for them (they are open core, so they also gate dozens of other features on paid plans). We didn't invent the idea.
For example, Mattermost's $10/user/month plan is proprietary software with roughly the features that Zulip provides as entirely FOSS (with a $3.50/user/month push notifications service).
By the way, since you mentioned Signal: Signal is great, but it's really just not comparable.
Signal is a SMS replacement/messenger app with minimal features that requires very low COGS per user, and launched with a $50M grant from a billionaire. Zulip is a team chat app designed to replace much more complex and capable products (Discord, Slack, Microsoft Teams).