Old Mac doesn’t want to update to the latest system—its hardware can’t handle it; old hardware should run old software.
However, macOS keeps prompting for updates, which is extremely annoying.
Blocking access to several domains involved in the update process by modifying the hosts file is a relatively convenient and easily reversible method.
For details, see How to Disable macOS 26Tahoe Updates—Prevent Computer Lag and Maintain macOS 15.7 | Bilibili.
There are also additional methods: 如何关闭macOS的自动更新提示