what verb tense is "having spent"

It's a participial phrase.

http://www.chompchomp.com/terms/participlephrase.htm

The verb tense "having spent" is an example of the present perfect continuous tense. This tense is formed by using the auxiliary verb "having" followed by the past participle of the main verb (in this case, "spent").

To determine the verb tense of a phrase like "having spent," you can follow these steps:
1. Identify the main verb: In this case, the main verb is "spent."
2. Note the helping verb: The helping verb in this case is "having."
3. Consider the form of the verb: The verb "spent" is the past participle form of the verb "spend."

Combining these elements, we can conclude that "having spent" is in the present perfect continuous tense.