At one point the limetri panel becomes inaccessible.
Which one, I honestly don't know. The only thing - I do not add several plugins with lumetri on the same timeline. Only one plugin, which is enabled by default, if you change something in its parameters. Resetting doesn't help revive the tools - lumetri > reset effect (all). Only "clear".
There is the Global FX Mute icon in the Program monitor, and that typically also has a keyboard shortcut. It's typically shown on the bottom left of the Program monitor controls. If blue, it's 'on' ... and all fx are off. Click or tap the right key-short, and it's gray ... off. And your fx are on.
On the adjustment timeline is ok, when on the main timeline addition is not available. I can remove the add-on timeline, but that won't make things better - the add-on will keep telling me that I don't want anything to do with you, Dimitri.
It could be the same story on another timeline. I'm just saying that it's not a fact that this whole thing happens because of some global add-on shutdowns. An add-on can be added second and subsequently one will be active and the other will be inaccessible after some time/after some specific action. As much as I've tried, I can't figure out what it is that I'm doing that makes an add-on unavailable.
By the way, I haven't found this switch. What you're talking about is sync settings?
Global fx Mute is a control available in the Program monitor. If it isn't visible on the controls at the bottom of the monitor, open the controls panel for that by clicking on the + lower right. Drag it to the controls.