Check Salesforce object and field access by querying EntityDefinition and EntityParticle

EntityDefinitions.apex

// Note that WITH USER_MODE is not allowed in Anonymous Apex!

List<EntityDefinition> entityDefinitions = [
      SELECT QualifiedApiName
      FROM EntityDefinition
      WITH USER_MODE
];

// Now entityDefinitions is a list of objects accessible by the current user, 
// a bit like Schema.getGlobalDescribe().keySet() but faster!

List<EntityDefinition> entityDefinitionsAndFields = [
      SELECT
              QualifiedApiName,
              (
                      SELECT QualifiedApiName, IsUpdatable, IsCalculated, Length, DataType, Label
                      FROM Particles
                      WHERE IsCompound = FALSE
              )
      FROM EntityDefinition
      WHERE QualifiedApiName IN :objectNames
      WITH USER_MODE
];
    
// Now entityDefinitionsAndFields is a list of objects and fields that the running user can access
// Don't call this with no filter in a big org or you might exceed the 50k query row limit