Can I make a claim for disability associated to a VA surgical botch after I left the service?

Taking it a piece at a time:
● Will it be covered as a service-connected injury (i.e., added to your rating)? No. But if you suffered an added disability while you were getting VA medical care, then you can file for a "1151 claim"*. A VSO may be knowledgeable in filing these, but if you are going to submit a FTCA claim (see below), then you should have your lawyer handle both of them because a 1151 claim could limit the scope of damages in a FTCA claim and you will need to ensure they are in synch.
● Regardless if the colonoscopy was related to a service-connected condition (since you are 50%+ on a disability rating, you're entitled to complete medical care from the VA), if there were errors committed during your colonoscopy that injured you or led to an injury, then you might have a malpractice claim*.
● Malpractice claims against the VA are handled under the Federal Tort Claims Act (FTCA)*. Military.com has a good write-up by a FTCA lawyer laying out the procedures you must follow on the administrative side to ensure you meet the timeline requirements (you MUST file a FTCA claim within two years of the incident, but must file an administrative claim with the VA first).
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* https://www.va.gov/disability/eligibility/special-claims/1151-claims-title-38/
* https://www.military.com/benefits/military-legal/what-you-need-know-about-winning-va-medical-malpractice-claim.html

I'm afraid to ask how you botch a colonoscopy, but I guess it is the VA.

Was the procedure related to the service connected disability, or not? If not, then I would say if the VA botched the attempted colonoscopy then you may have a medical malpractice claim, which would fall under the Federal Tort Claims act, and you have two years from the injury was known or should have been known. But to bring up such an action you would have to show negligence in the standard of care was grossly deviated from.