I think the more expensive tests are covered in plastic so that you can hold them easily and direct them into the stream of urine, and also the window is clearly identified which helps with easy reading. With the small test strips, you need to wee into a clean container and then dip them. Interestingly doctors' offices often seem to use disposable plastic cups for this purpose, but of course you can use anything you like at home.
I think a snot sucker can defo be avoided - they weren't even a thing when I had DS apart from on American forums, they weren't heard of over here and babies all managed without them.
I used teaspoons and did baby led weaning, so no plastic baby spoons. We did have little sets of toddler cutlery which had plastic handles.
I did use beakers, but you don't have to - you can use metal cups for non-breaking (expensive though) or just normal mugs and thick glasses with supervision. Or if you've got a few baby bottles already you can often get sets which turn into beakers later with just a different top, that would reduce use of plastics.
Baby bottles can be purchased in glass very readily these days. I had plastic ones - but if you get wide neck ones, these are actually quite useful after their life has been completed, as 8 fluid ounces is the same as a cup measurement, and hence 4 = half, 2 = quarter - so I used them for years as measuring cups in the kitchen, until they eventually all went missing or got broken.
You can definitely kit a child out entirely in second hand clothes if you're organised, and avoid plastic toys which aren't long lasting. Of course, you can't do much about gifts or party bags received from others. You can talk to your own children about the wastefulness of magazine freebie toys or McDonald's toys etc, and do non-plastic options for party bags for your own children's parties such as giving away small books from a multipack, packets of crayons, those little "magic towel" things, etc, even a craft project the children have made themselves.