I haven't been able to get an airliner to follow the flightplan, I don't know if that's something I'm doing wrong or the sim.
I'm having a blast with the 737 Max 8 passenger version, using a freeware TUI livery from FS.to. I'm currently flying it from EGNM Leeds Bradford to LEMG Malaga. There's a knack to it, here's my procedure:
Create a flight plan with the MSFS2024 web browser flight planner - I select the 737 Max passenger version first, then select my departure and arrival. I then auto-select all sections inbetween. If any section appears on the map in red, there's a problem and I remove that section before saving the flight plan. No need to worry about entering weights and fuel, they don't carry over into the sim (yet).
Launch the sim, select the 737 Max, configure the passenger variant, then the livery, then the registration, callsign and flight number.
Return to the world map screen to select live weather and set the time as required.
Open the EFB, go to the flight plan screen and select Load Plan, e.g. EGNM-LEMG is the latest one I've saved. Scroll to the bottom of that screen and click on Send to ATC (wait a few seconds for the button colour to change back to light blue), then click on Send to Avionics and wait again. Go to the aircraft screen and enter your payload and fuel details, then click on Load in Aircraft. Finally, close the EFB.
I always start my flights on the runway, and once in the cockpit I go to the built-in EFB below the left window, scroll down to bottom of the flight plan list and click on Send to Avionics again. This sends the flight plan to the FMS.
Next, I go to the FMS and click on the Legs button to check for any Discontinuity. I click the Next Page button and delete any Discontinuity I find before clicking the Exec button. The flight plan is now active in the FMS and on the displays.
I always set the AP Heading to the runway heading before takeoff so that during climb out, when I engage AP CMD, I can select AP HDG before switching to AP LNAV. Sometimes LNAV won't engage on it's own, but always does when HDG is engaged first.
Hope this helps!