When you do the Windows [restart] or [shut down] followed by starting normally, as you saying the Bluetooth doesn’t come on automatically, or are you saying that when you go to the Bluetooth control panel / Settings screen you can’t turn it on at all; it simply won’t turn on? Does it look turned on, e.g. slider goes to the active color, or it it stuck grayed out or in the off position? If it does appear to turn on, how are you deciding that it’s actually not? Just by the mouse not working or is there other evidence?
When you say Settings show the mouse and speaker are connected, is this after Bluetooth just died, or is this after one of the normal restarts that don’t actually bring Bluetooth back?
Also, do both mouse and speakers always fail simultaneously, or can it ever be just one or the other. I’m considering the possibility that your Bluetooth isn’t actually shutting down, but rather is doing something to blink off for a bit, which causes the mouse or speakers to lose their connection and they don’t notice when it comes back. What happens if, after Bluetooth seems to shut down, you power-cycle the mouse, speakers, or both. Does that cause a reconnection or does nothing happen?
At the risk of a silly question, have you tried deleting the mouse and speakers from the Bluetooth device list then re-pairing them?
I have had vaguely similar situations with other hardware on other PCs over the years. Where only an extra-thorough reboot got stuff going again. The usual culprit is a shit device driver and/or shit device that is prone to crashing into a state where only a full hardware reset unjams whatever is fouled up. Unfortunately, drivers are provided by the device manufacturer and are frequently not well-maintained.
Trying to check for updated drivers from Lenovo via their website, or Windows update, or any Lenovo-branded maintenance app that may have come with the laptop are your best bets. If that comes up empty, the next most likely problem is hardware, which probably means replacing the laptop if you really, really need built-in Bluetooth; something like built-in Bluetooth is generally not easy / practical to fix.
If it gets that far that you’re considering replacing the laptop, something else you can consider is disabling the built-in Bluetooth features and buying a separate Bluetooth transceiver. They can be had for cheap. Amazon.com : usb bluetooth adapter for pc. Assuming you have an available USB port on your laptop you can dedicate to this use. I had an older laptop that came out just before built-in Bluetooth became universal. I ran for years with one of these teeny Bluetooth adapters; worked great.
That’s bypassing your problem rather than fixing it, but for sure $15-20 is a lot better than $500-1000 for a laptop. Also far less hassle to move into.