What i would do is check each individual part of the system. The goal here is to verify each component is not resisting the change up to the largest ring.
Check the derailleur movement. As your bike has exposed cables you can wrap a rag around the front shifter cable and pull it away from the down-tube, which will actuate the derailleur. Put the shifter in the low gear position and try getting the chain to shift up to the big ring while pulling the cable. (You may need a someone to help pull the cable or manually turn the cranks). If the derailleur will not shift the chain up, its possible the high limit is set too low, there is something jamming the mechanism, or the derailleur may not be positioned quite right.
Another check you can do is shift to the high gear position, and check if the derailleur is jammed up hard against a stop by trying too plush it outwards. If this is the case the shifter is not moving the derailleur, it’s stretching the cable.
If you can get the derailleur to shift the chain reliably by manually pulling on the cable check the shifter and cable. Disconnect the cable from the derailleur. Hold the cable with pliers, apply some tension and work the shifter. The cable should be pulled in and pay out smoothly. Sometimes one or two strands of the cable break and these can hang up in the housing or shifter.
If this get resistance, remove the cable from the housing right up to the shifter and check again, also inspect the cable.
Running through a step by step derailleur setup process can also be helpful. Park Tool Repair has a great set of step by step instructions for many bike maintenance and adjustment issues. https://www.parktool.com/blog/repair-help/front-derailleur-adjustment.
If you solve the shifting resistance issue but still find the upshift is unreliable, I’ve found that sometimes toeing out the rear of the cage slightly helps upshifts.