I improved 260 points from my last SAT. Do colleges care or no?
Only to the extent that colleges use the highest test scores to determine admission when you submit multiple tests.
Good for you - that’s a nice leap in an overall score! Your highest composite score; highest scores taken from each area across several tests are taken to get a total score, is important. Many colleges ‘superscore’ - this is what it means to take the best score from each section despite the tests being taken at different times and adding them together for a total score. An improvement on your overall score is always good and colleges do care or there would be no need to take the SAT at all!
There are some schools that really only pay attention to the CR and Math sections though, so if all your improvement was in the Writing section - for some uses - this may not be as valuable. For example, some honors colleges require a certain SAT in CR and Math only to be eligible for admission - no matter what the overall SAT score of the applicant may be, you’d have to have that number to apply.