My dad always has his phone on the table at restaurants. He says it's not a big deal to glance at it if you're waiting for a call. Ngl, we probably stress about this stuff way too much.
Try putting it in your pocket on silent. You still feel the buzz if it's important but you're not tempted to check every notification. It keeps you present without the stress.
Keeping it under the table like @wyattp45 said is key, it stops you from looking down at it too obviously. It helps you avoid eye contact when things get awkward too. Makes the whole thing way less stressful.