On LineageOS (which ships without Google Play Services), WhatsApp keeps re-showing the "Google storage backup / Back up to your Google Account" prompt because it can't find a Google account, and there's unfortunately no "never ask again" button. Here's what actually works:

1. Set the schedule to Never (main fix)

If you can reach the screen: WhatsApp ⋮ > Settings > Chats > Chat backup > Back up to your Google Account > backup schedule > "Never" (or "Only when I tap Back up"). WhatsApp's own docs confirm "Never" is a supported schedule; once saved, the nagging stops and only local backups (2 AM daily, in Android/media/com.whatsapp/) continue (WhatsApp Help Center).

2. If the screen is stuck/unreachable without a Google account

On a de-Googled ROM the backup settings page sometimes can't complete because there's no account to select — a known pain point with WhatsApp on LineageOS (Reddit r/LineageOS). Two workarounds:

• microG route: if you use LineageOS for microG, sign into a Google account in microG (microG Settings > Google Account, and enable "Allow apps to find accounts" in the Google Account Manager view). WhatsApp then sees an account, you open Chat backup, pick the account once, set frequency to Never — the prompt stops permanently.
• Without microG: you can't satisfy the prompt, and there is no built-in way to disable the in-app banner forever. Your best mitigation is to suppress it at the notification level: long-press the notification > gear icon > disable that notification channel (LineageOS has per-channel toggles). The in-app occasional banner may still appear, but you'll never be notified again.

3. If it's the persistent notification (not the banner)

If what you're seeing is a lingering "Google storage backup" notification rather than a popup: force-stop WhatsApp (Settings > Apps > WhatsApp > Force stop); if a backup is half-configured, that clears the stuck notification (XDA Forums). Then apply step 1 or 2.

Bottom line: there's no official "stop proposing forever" toggle — the reliable permanent fix is to give WhatsApp a Google account once (via microG) and immediately set the backup frequency to Never. Without microG, blocking the notification channel is the closest you can get.