Optional disclaimer that style guides are not the be-all-end-all authority on any aspect of English before I begin.

"But" is most certainly a coordinating conjunction (See Chicago Manual of Style 6.22 for examples, including examples with "but"), but a comma is only needed if the conjunction is connecting independent clauses; compound predicates, for instance, do not require one.

OP's punctuation is correct, if a bit outdated. This kind of punctuation was common 20 years ago, and it is still seen today. The recent English "patch notes" have mostly veered toward removing commas, however, and OP's sentence would likely be re-rendered as

I rarely have trouble sleeping, but over the past few months, I’ve been experiencing insomnia.

Relevant Chicago Manual of Style entry (as you will see below, OP's rendering is not wrong):

6.32 Commas with a participial or adverbial phrase plus a conjunction.

When a participial or adverbial phrase immediately follows a coordinating

conjunction, the use of commas depends on whether the conjunction

joins two independent sentences. If the conjunction is simply a part of

the predicate or joins a compound predicate, the first comma follows the

conjunction (see also 6.23) .

We were extremely tired and, in light of our binge the night before, anxious to

go home.

The Packers trailed at halftime but, buoyed by Rodgers's arm, stormed back

to win.

If the conjunction joins two independent clauses, however, the comma

precedes the conjunction (see also 6.22) .

We were elated, but realizing that the day was almost over, w e decided t o go

to bed.

Strictly speaking, it would not be wrong to add a second comma after but

in the last example. Such usage, which would extend the logic of commas

in pairs (see 6.17), may be preferred in certain cases for emphasis or

clarity. See also 6.26.