There's still dogs being signed over, but the numbers are only just beginning to creep up I think. As others have said, many people have spent silly money on dogs, so any dog under a year old right now they want to recoup those losses.
A lot of dogs being signed over to rescue may have behavioural issues like separation anxiety or lack of socialisation with other dogs making them nervous or reactive. There's lots of sad health issues I've seen recently as well.
Rescues are very busy but there will be a lot of dogs "in the wings" so to speak, who may need vets or behavioural work before they're available, or they're reserved so fast they either never make it to the website or are on the website for all of 5 minutes.
Everyone wants easy dogs, dogs that can live with kids or other pets, dogs that can live in flats without gardens, but that's not what is being signed over. I'm sure I've read of some rescues with no dogs available for adoption, but full kennels, all the dogs they have need extensive behavioural work before they can be rehomed.
A responsible rescue is not going to rehome an extremely excitable dog, or a dog with bite history, or a dog that pulls like a tank on the lead, or a dog that's reactive to other dogs, to a family with young kids.