Today there are five constellations of GNSS systems. GPS is just one of the constellations. Most modern systems are capable of tuning more than one system and many will tune SVs from multiple systems to get the best possible solution. With SBAS most receivers have the ability to track at least 24 satellites, although some of those will be the GEO SVs.
The chances that all five constellations will be unsuitable for navigation is highly unlikely. Your biggest threat to GNSS navigation is RF spectrum interference. Not all countries protect the GNSS frequency spectrum or will actively interfere with it. Warzones are a perfect example of when a country will actively interfere with GNSS. While GNSS is the easier signal to interfere with there have also been cases where countries that have actively spoofed VOR and NDB signals. The bottom line here is you have to be aware of where you are flying and what is going on below you.
Most advanced navigation systems use multisensor input to the navigation solution. These navigation systems are not pure GNSS solutions, just they use GNSS as one of the inputs and then compare the location provided with the other sensors usually through a Kalman filter. They will include dead reckoning through the ADC/AHRS, VOR-DME, DME-DME, and usually will have input from an IRU/INS. Most business aircraft and airlines will use these types of navigation systems. So even if GNSS is interfered with they can continue to provide a navigation solution. Although that solution may not meet approach criteria.
A part of any modern instrument courseware should be instruction on what to do if you ever get the dreaded integrity message or light on your avionics. If you have not received formal instruction on this then I would encourage you to contact your local CFII and plan some training. This is something that can easily be covered in an hour of ground time and followed up in an ATD for low-cost training. I know our Full Flight SImulators are capable of degraded SBAS and GNSS operations, but it is not part of the standard recurrent syllabus so the client must request it.
BTW, the current status of the U.S. GPS system can be checked here: GPS Constellation | Navigation Center and I cannot recall an instance where the entire system was down. With S/A turned off and 31 SVs in orbit the system is fairly healthy and unlikely to face an SV based outage.