Zagg and OtterBox are arguably amongst the better manufacturers of tempered glass screen protectors - with good reputation. Always choose a screen protector from a well known brand - choosing a screen protector that is specifically designed for your iPad model.
While a properly designed screen protector will always cover the illuminated/active area of the screen and the majority of the screen bezel, you should not expect complete edge-to-edge coverage. Many well designed screen protectors will be described as "case friendly" - and will be slightly smaller than the overall size of the screen and its surrounding bezel. Being slightly smaller than the overall size of the screen/bezel, the marginal gap around the periphery accommodates the tiny "lip" used by many fitted cases to retain the iPad.
Glass Screen Protectors will also usually feature cutout areas that correspond with the front-facing camera, the FaceID sensor array and pinhole microphone - as applicable for the specific iPad model.
Unlike film-based Screen Protectors, laminated glass versions can provide a significant degree of screen-impact protection - some makes being particularly better in this regard than others. By example, Zagg and OtterBox screen protectors are designed with impact protection in mind, the glass element of the laminated construction being made from toughened glass.
Screen protectors offer a secondary benefit in that should worst occur - and the screen shatter - broken glass is retained reducing the potential for personal injury.
Use of a screen protector is largely personal choice - but there are considerations.
iPad screens are robust, but the anti-reflection treatment and oleophobic coating can be easily damaged by tiny grit/dust particles that are unavoidable in many environments. The oleophobic coating is a chemical sacrificial layer that will wear-out over time.
Your iPad screen is the single most expensive component of your iPad - whereas a screen protector is sacrificial layer that, if damaged, is easy and relatively cheap to replace. A screen protector is not, necessarily, a substitute for an AppleCare+ plan - however, the cost of good quality screen protector is substantially less than an AppleCare+ plan.
If budget allows, AppleCare+ and a good screen protector are complementary products. If the worst were to occur, AppleCare+ can [literally] pick up the pieces, whereas a scratched or surface-damaged screen protector can be replaced for less than the cost of the AppleCare+ deductible fee that will be charged if a claim is made.