My SIL will ask my children around for supper without asking us. I know it’s silly but it makes me feel like she’s stealing them away from me, it makes me feel displaced/competitive…
Your children are adults. Neither they nor your SiL need your permission to have supper together.
Your children are not extensions of you, they are autonomous humans in their own right, & your feelings of displacement indicate an unhealthy enmeshment. Maybe this feeling is the signal you need to start detaching a little, & being happy that you have raised children who have a healthy relationship with their aunt.
The competitive feeling is more concerning. Almost like you feel SiL has no right to 'play' with your children without your gracious dispensation, which you maybe feel entitled to offer or withdraw because you, with your superior child-bearing status, ought to be the one in the driving seat of who is allowed to spend time with your offspring.
Almost as if you feel you have been "Wendied" by SiL.
My own sister was like this with her young adult DC.
Nose right out of joint when I took my nephew for our first pint together. How dare the established order be rocked! How dare a spontaneous plan happen without her express control organisation & permission! It was all connected with how astonishingly controlling she is of her DC & DH.
I do hope that's not the same deep seated motivation for you, & that it's a less sinister, more understandable, feeling of wondering who you are & what your role is now the DC have grown.
If this is more connected with a generalised insecurity (maybe you were a SAHM for many years, so your identity is still closely connected to your DC's movements through the world) - don't worry, it will pass, as you re-establish your own career & interests now you have time to be fully yourself again.
If, however, it's because you feel that you have been able to Queen Bee it over a child free woman (interesting that you opened with that - it's entirely unrelated to how she & your DC interact together, they are not her substitutes for 'failing' to achieve parturition ffs), it's likely that you see your DC as pawns to reflect & broadcast you ego, & you need to let go of that, stop believing that it's up to you to control anybody's relationship with anybody else, & do it sharpish before you push your DC away with overbearing possessiveness.