$^{13}$CO and potential variability in $\beta$ Pictoris b with GRAVITY+

The $^{12}$CO/$^{13}$CO ratio was introduced as an indicator for where in the disk a planet has formed. Previously a lower value compared to the host star's was suggested to show that a planet accreted CO ice beyond the disk's CO ice line. In this letter we aim to determine the $^{12}$CO/$^{13}$CO value of the directly imaged planet $\beta$ Pictoris b, and whether we can link it to its formation. Its apparent brightness results in an exceptional S/N of up to ~60 per wavelength point. We present the first science observations with the upgraded GRAVITY+ instrument at a spectral resolution of R ~ 4000, which we analyse with petitRADTRANS. Our retrievals robustly indicate the presence of $^{13}$CO with a $^{12}$CO/$^{13}$CO ratio of 91$^{+24}_{-17}$, consistent with both a solar to ISM-like value. Our $^{12}$CO/$^{13}$CO value corroborates recent interpretations that $^{13}$CO may be a less useful tracer of formation location in the disk than previously thought; nonetheless, we discuss theories with which this value is consistent. As our observations span ~7 hours, this enabled us to search for atmospheric variability in $\beta$ Pictoris b; we report a tentative constraint on the variability amplitude of about 1.4$^{+0.6}_{-0.7}$%.