Reference
What it costs to run
You pay the provider, once per string, and the numbers are on your account page.
The shape of the bill
A string is translated once and then served from the database. So the cost is the size of your site, once, per language, plus whatever you change afterwards.
There is no per-view cost, no per-visitor cost and no floor. A site nobody edits costs nothing to keep translated.
Where the money goes
Almost all of it is the bulk model doing the first run. That is why there are two model settings: the interactive one is used for the handful of strings you trigger yourself, and the cheap one for the thousands nobody looks at individually.
Your licence page breaks the spend down by provider and by model, so the question "is the expensive model earning its keep" has an answer rather than an opinion.
Keeping it bounded
The monthly budget stops new work at a number you set. The batch size, requests per minute and tokens per minute settings shape how fast the money is spent rather than how much.
On Anthropic, the batch API is used by default for bulk work, which is roughly half price in exchange for not being immediate. Interactive work never uses it.