Sorry to hear about the adductor/groin strain. If you’ve ruled out the other issues then full on rest should be limited to as short a period as possible to avoid muscle atrophy and loss of function. Strains and tendinopathies heal with the right amount of stress applied to them and complete rest is rarely the answer. You can start by working toward regaining full range of motion and incorporating in some soft tissue work to desensitize the area:
Next, progressive loading will be important, but training should be performed within the limits of pain. We need to start to build some capacity in that tendon/tissue. You can start with some isometric holds (squeezing a ball or object between the knees) and side lying adductor leg raises. Then progress to an exercise like a lateral lunge to increase load on the adductor. This is a time where tempo work will also be your friend with an emphasis on slowing everything down. I’d start with something like a 3-1-3 or 5-1-5 tempo (3-5 seconds up, 1 second pause, 3-5 seconds down). In the beginning I would start with bodyweight. Have the affected leg straight and lower down into the lunge till there is a gentle stretch/tension in the groin area. Work towards gaining some pain free ROM and once you can work up to some higher reps you can start incorporating some weight to the movement. You can incorporate other non-aggravating exercises like glute bridges, sumo squats, step ups, etc but again emphasis with starting slow with tempo work being your best bet. Keep slowly building capacity and work out any strength deficits from side to side. As you progress in strength and tolerance, I like using the Copenhagen plank as litmus test for any strength deficits side to side. Work towards being able to hold the plank for equal duration on both the affected and non-affected side. Cheers and good luck!