I can see your point of view, but I also don't think they are being unreasonable either!
For Christmas my mum has got my 20 month old DS a balance bike, a tablet, games, books, flash cards, paint and craft things, clothes. She has also spent 45 pounds on 2 different advent calenders for him, I think she is nuts personally but she loves buying him stuff.
I think another reason she buys so much is I'm a SAHM so money is tight and she doesn't want me to stress about buying him lots at Christmas. I think it's obscene tbh the amount of stuff he's going to end up with as his other grandma and his grandads also go overboard! Our presents for him will never compete money-wise with the gifts off DS's grandparents as we are at a different stage of life to them.
We are getting him some Peppa pig toys, a kitchen and food & a few books! And most of it will be second hand.
Would your PIL be doing this from a place of kindness? I know you said money is tight as you have a newborn, maybe they are trying to take some of the financial burden off you?
Just think in 30 years time you could be the grandma wanting to buy your grandchildren things for Christmas. I know it's hard to see past the fact you wanted to buy your DD her first bike, but it honestly doesn't matter in the grand scheme of things, you will most likely be the one teaching her to ride the bike and that's what she will remember more than who bought it!