Don't worry about them just run your rotary mower over them.

While they will not be shredded completely, the will be broken down to s size that will fall into the grass. As the decompose, which because of the size is fairly quick, they will help build up the soil.

The other option is a leaf rake, a pitch fork and a strong back. Depending on the size of your yard, hand raking could be a big job.

A rake, or if it's a big flat area, a push-propelled lawn "sweeper". It's like those manual carpet sweepers with rotating brushes, but for a lawn.

The small stuff decomposes quickly in compost heaps

I empathize with you, there's a yellow birch in the back yard, and every now and then it deposits a lot of small twigs and stuff juuust too big to mow over. I don't mind mowing but raking is a fall activity. Like most urban locales burning yard waste is technically verboten, adding to the hassle. Our clean yards aren't typical, they will quickly revert back to Wilderness ha ha

I run a low mulching mower over mine. I have a chipper shredder with a low intake on the front and sometimes I rake, shred and compost the debris.