Monitor , Office Laptop & Mac Mini

You could look for a HDMI switch – something like this:

https://www.amazon.com/Switcher-Splitter-Automatic-Support-HDCP1-4/dp/B09MM5QT3R

There are lots of these kinds of switches on Amazon. There are also more elaborate KVM switches that switch USB connections (for a wired mouse and keyboard) as well as HDMI. If your BenQ monitor is a 4K monitor, one thing to check would be whether a switch supports 4K, and if so, at what refresh rate. (The one above supposedly supports 4K, but at 30 Hz.)

If your work laptop has a USB-C port with support for USB data transfers and DisplayPort ALT mode, another possibility might be to get a USB-C dock with a HDMI output port, and to transfer the USB-C plug between the Mac Mini and the work laptop as needed. Moving USB-C cables in this way would be more awkward for a Mac Mini than for a Mac laptop, given that the Mini's USB-C ports are on its back side.

when I ran out of input sources on my monitor and got sick of climbing up on the table to pull out a hdmi cable and insert another when working from home, then I just go myself a hdmi switch The 6 Best HDMI Switchers of 2023 (lifewire.com)

it was a pretty cheap one with a physical button and only 2 inputs it did the job just fine.

If your BenQ monitor has other types of video inputs (e.g., DisplayPort, Mini DisplayPort, USB-C (DisplayPort)) in addition to its "one HDMI slot," you might want to consider taking advantage of that.

The M2 Mini has USB-C (DisplayPort) output, and you can find lots of adapters and adapter cables that go from USB-C (DisplayPort) to standard DisplayPort or Mini DisplayPort connectors. Use the applicable connection method to hook up your M2 Mini to your BenQ monitor, so the work laptop can have the monitor's HDMI port all to itself. Then use the input switching controls on the monitor.