What you mention at first is correct, however, none of it really applies here (~てある also isn't equivalent to what's seen here since ~ておる = ~ている but I digress).
"お支払いは現金のみとなっております" is just equal to "お支払いは現金のみです." Why is this? Well, "となっております" is really just a business/part-time job form (or バイト/マニュアル敬語 as it's called in Japanese) of "です;" in fact, looking up the Wikipedia article for "manual keigo" shows this exact form.
Manual keigo is, depending on who you ask, a slightly skewed version of keigo mostly used in part-time jobs where certain expressions are used to "sound" polite despite not really being fully accepted keigo.
Now then, the keigo: おる is 謙譲語 however it is not regular 謙譲語 (i.e. 謙譲語1) but 謙譲語2 (or 丁重語). 謙譲語2 is, for all intents and purposes, just an even more polite/formal version of 丁寧語, which is also why you never use the verbs associated with it in plain form, always ます-form.
(If you want to go deeper into all things keigo, I highly recommend this YouTube playlist by a native Japanese speaker who explains all the different forms and usage cases of keigo.)
So, for a full breakdown of the sentence:
- お支払い – payment
- は – topic particle
- 現金 – cash
- となっております – is/copula
This then gives us the translation "we only accept payments in cash." Breaking the sentence down further than this isn't really necessary since it follows manual keigo basically to a tee as I see it.
As you can probably tell, I'm not really sure I agree with the translation Tofugu gave for this sentence. Why they translated it like they did I have no clue, but, if I'd hazard a guess, I'd assume it's to get across the "formality" of the keigo in the sentence in their translation. Though, for actually understanding the sentence, their translation really doesn't help much in my opinion.
て[あ]{L}る is for resulting actions "in preparation for something", but are asking about ~て[お]{L}る. – istrasci Apr 13 '21 at 15:35