Definitely do linoleum and do glue it down everywhere. Caulk it all around the perimeter for future possibility of hosing out coop once a year. Cheap and does not retain odors or bacteria. Then whether you go with a tarp or whatever, you will have a floor underneath that will last.
Consider a poop plank, lino over OSB and 24" wide. full length of the roost. If you scrape it daily
you will remove 95 % of the source of odors, humidity, and fumes from your coop, AND your litter will last a year. Do not worry about streaks
because they quickly dry to where they do not stink, and because the chickens do not notice nor care.
I am still using grass clippings and expect them to last a year. I add to them a little all during the grass cutting season and the coop smells so nice. Best of all, they are free. I would not change over because they have done so well for me. If I could get free wood chips, I would use those too.
If the poop plank is not to your liking, you can change over to a tarp system and doing litter as often as you like. Always wear a dust mask when working with changing litter.