Most routers have a web interface where you can see all the devices currently connected. You go to the router's address (usually 192.168.1.1 or 192.168.0.1, check the back of the device) with the username and password (if you've never changed it, it's probably admin/admin or something similar), and look for a section that says "connected devices," "DHCP clients," or "clients." If you see devices you don't recognize, something's up. It's also worth checking the connection history if the router allows it.
Now, your speed dropping and disconnections don't necessarily mean you've been hacked. It could be Wi-Fi interference (if you live in a building with lots of nearby networks), the router being bogged down by automatic updates, or simply degradation after years of use. The first thing I'd do is restart the router, wait a couple of minutes, and test again. If you're still having issues, try changing the Wi-Fi channel from that same interface (sometimes 1, 6, or 11 work better) or call your provider to have them verify from their end if you're actually getting those 300 Mbps.
Either way, even if you don't find any intruders, it's smart to change your Wi-Fi password to something strong (varied characters, no obvious words) and review what security methods you're using. WPA3 is the best if your router supports it, then WPA2, never WEP. And another thing: if the router has a reset button, consider doing it if the speed is still low; sometimes the configuration gets corrupted. But rule out the simple stuff first before assuming the worst.