You can disable the feature, it's called something like near device discovery.
Also check this cool app that lets you spoof those devices and spam the suggestions.
Search through your settings for a "Quick Pair" or "Fast Pair" option. Turn it OFF. Do not leave it turned on except during times when you're wanting to use a known device you've bought new that supports the feature.
Turn the feature off when not setting up new devices to work with other devices.
For anyone running a ROM based very closely on AOSP, the ability to disable Fast Pair was sadly not built into the OS until Android 14
Before Android 14, it is possible that Google has backported this setting to your device using Play Services. It can be found under Google Settings, Devices and sharing, Devices, and "Show Notifications"
Why is this getting downvoted? I get that it doesn't provide a reasonable solution for most people, but I think they have a point. Bluetooth itself is anything but private or secure, and you should at least disable it while no devices are connected.