TV is soooooooooooooo different from the screens on our phones and tablets. For babies and toddlers, the screens they need to be kept away from are those intense screens.
On television, high quality children's TV is crafted to support their development and to be an experience that you share and engage in. You sing along, the characters ask you to answer back, they do crafts and recipes to copy at home, they look at literacy and numeracy. Good quality children's TV (I'm thinking of CBeebies) is so incredibly researched into how children communicate and develop speech and language, it's slower paced, the music is plinky plonky, they use repetition and pattern.
This is the opposite of the YouTube slop.
If I babysit my nephews for a few hours we will always do something fun and constructive because I can give them all my energy for that time. If it were my own children, yes they watched TV for a bit while I did a chore or we sat down together for a half hour with a drink and a snack after a busy physical day.
I hate and I do judge parents who ram a screen in front of a baby or toddler in situations where they could be engaging with the world around them. I know where the screen fear comes from. My kids didn't use them because the older ones were around before the technology was there and with my youngest we just didn't use them because it wasn't our norm. I NEVER EVER EVER let my kids have my phone. I see parents let their children take their phones ALL THE BLOODY TIME to watch videos or use apps and it's crazy to me! This expensive bit of kit with most of my life on it?! No, that's MY phone so it stays in MY pocket or bag. Boundaries.
Also, this is 2 hours. 2 hours, it's nothing.
He's 7 months old, even as a TV using mum that's waaaay too young to have left him in a room on his own watching the big screen in the corner of the room. Mine were around a telly at that age but not really actively WATCHING it. Breastfeeding while watching Countdown? Sure, I don't know what damage would've been done to their brains then.
Final thing, this is a kind favour from your neighbour. One thing about other people looking after your child is that you've got to trust them. From your description she knows what she's doing and they'll have a lovely time together.
I hope you have a fabulous time out together as a couple!