Is there a metric for “evolutionary agility”?
Yes, there is a measurement laid out by Haldane (1949) called 'Darwins'. One Darwin is given an $e$ fold change in a trait over the period of 1 million years.
As to your second point, yes there are different variables which control the rate of adaptation within a population. The classic factor is genetic variation, as given by Fisher's (1958) fundamental theorem of natural selection, which states:

The rate of increase in fitness of any organism at any time is equal
to its genetic variance in fitness at that time

So broadly speaking, individuals with more additive genetic variation will adapt more rapidly.
Of course, there are many other factors such as generation time, effective population size and mutation rate will influence the response to selection. However, such as in the case of generation time, the relationship is not necessarily a simple one (Gandon and Mikalakis, 2002).
EDIT
After re-reading your question, I think I perhaps misunderstood it.
I suppose the term you are looking for is 'evolutionary potential', which is defined by Steeves et al (2017) as:

The capacity of a population to evolve in response to environmental
change.

There is a nice chapter in this book which gives a good overview of the topic. The chapter may perhaps be available for free on certain websites.
References

Haldane, John Burdon Sanderson. &quot;Suggestions as to quantitative measurement of rates of evolution.&quot; Evolution (1949): 51-56.
Fisher, Ronald Aylmer. The genetical theory of natural selection. Рипол Классик, 1958.
Gandon, Sylvain, and Y. Michalakis. &quot;Local adaptation, evolutionary potential and host–parasite coevolution: interactions between migration, mutation, population size and generation time.&quot; Journal of Evolutionary Biology 15.3 (2002): 451-462.
Steeves, Tammy E., Jeff A. Johnson, and Marie L. Hale. &quot;Maximising evolutionary potential in functional proxies for extinct species: a conservation genetic perspective on de‐extinction.&quot; Functional Ecology 31.5 (2017): 1032-1040.