How long have U had her? - Since puphood, or did she arrive as a teen or young-adult?
Anxiety can be, as already mentioned, inherited / genetic - but that should have been apparent early on.
I am presuming that for some unspecified while, her behavior was 'normal' or at least in the normal range, as it seems that her behavior changed, correct? - & that's when U became concerned.
Anxiety can also be a symptom of a medical issue - hypothyroid can affect behavior, but *usually* hypothyroid manifests more as "irritability" than anxious - dogs act cranky, stuff that didn't used to bother them now does, they have a lower threshold of tolerance than their usual self.
A racing or erratic heartbeat [one symptom of Lyme disease] can defo provoke anxiety in dogs, just as it does in humans - in Lyme cases, the cardiac symptoms are often worst AT NIGHT, so the vet may not witness them.
One complication of anxiety caused by environmental stimuli:
Dogs can hear a far-greater range of frequencies than humans can, well into infrasonic & ultrasonic... so noises that upset a dog can be completely UN-heard by humans. // Don't assume that if U can't hear anything, the dog shouldn't, either.
Some of the common audio-irritants for dogs: digital clocks, fluorescent light bulbs, compressors [used in refrigerators - Coke machines, the household 'frig, refrigerated tractor-trailer rigs, etc], sodium-vapor lamps, ultrasonic humidifiers, distant thunder [infrasonic - dogs can hear an approaching storm while it's still over 5-miles off, just how far depends on the intensity of the lightning generated], over-amped bass notes, the scream of sirens...
Some dogs develop unfortunate associations
that amount to superstitions:
something BAD happens by sheer coincidence at the same time as something perfectly innocuous - the dog concludes that the 'everyday' thing is connected to, possibly even the CAUSE of, the bad event.
So the innocuous event becomes worrying, or even terrifying.
One such pairing involved the thermostat switch for the heating / cooling system of a client's house, but it took awhile to figure that out - we only knew that Spring & Fall, the dog was normal; winter & summer, he became increasingly anxious, pacing, drooling, whining subvocally, & seeking contact reassurance constantly.
They shut off the HVAC to clean the vents, & suddenly from being a needy noodge, their anxious dog became chilled-out & calm; now we had WHAT, but not WHY.
No matter - we just deliberately set out to pair the soft click of the switch with every wonderful event we could think of, from ice-cream to fetch games, & within 3 or 4 weeks, he didn't even seem to notice it anymore.
I would certainly NOT predict or expect that a new dog nearby that Ur dog enjoys play with, would cause
anxiety - that makes no sense. If anything, more social contacts create greater emotional resilience & better rebound from stress.
So IMO - no; the new dog is not "causing" stress, but is very likely reducing it.