That's not clear from any data on 'a real infection'. The phrase 'against infection' masks the fact that the vaccine is nearly totally effective against hospitalization (or worse) due to infection. It saves your life, but you still cough.
That's a complete nonsequitur. Vaccine immunity works in the bloodstream, and the communicable virus is in the respiratory tissues, so isn't quick to respond. Delta gained in scope by its own highly-transmissible nature, not in any way assisted by immunity nor by a vaccine.
Maybe mask requirement lapses created delta.