What is the optimal version of Metroid Dread for speedruns? Physical version, digital on console or digital on microSD?

Digital installed onto switches internal memory. You also save a bit of time if you remove your SD card all together. Version 1.0 is also a bit faster than 1.01 but most people are running on version 1.01

digital on your internal memory is the fastest but version 1.0.2 is the only legal version currently

I have only the physical version. Is it possible to install the game from cartridge it to my internal memory card?

If you have a modded switch you can rip the game cart to a .xci - then install the package onto your switch, should be similar load times to the digital version.