Tantum abest ut vapor maneat, ut per laconicum pervagetur.

This is an idiomatic Latin construction.

A good way to understand it is:

• tantum abest ut X, ut Y
  = it is so far from being the case that X, that instead Y
• more naturally in English: far from X, Y happens instead

So here:

• ut vapor maneat = that the steam remains
• ut per laconicum pervagetur = that it spreads through the steam room

The whole sentence sets up a strong contrast: the steam does not stay put at all; rather, it spreads throughout the room.

Because they are doing two different jobs within one fixed pattern.

• The first ut introduces the thing denied or rejected: ut vapor maneat
• The second ut introduces the actual consequence or opposite reality: ut per laconicum pervagetur

So the structure is not just random repetition. It is the standard pattern of this idiom:

• so far from X
• that instead Y

Both verbs are in subjunctive because they are in ut-clauses used in this idiomatic construction.

More specifically:

• maneat is present subjunctive of maneo
• pervagetur is present subjunctive of pervagor

The main verb is abest, which is present tense, so Latin normally uses the present subjunctive in dependent clauses after a primary tense.

So this is not a case where the subjunctive means doubt or unreality in the English sense. It is mainly there because Latin grammar requires it in this construction.

The subject of both verbs is vapor.

So Latin is saying:

• vapor maneat = the steam remains
• vapor per laconicum pervagetur = the steam spreads through the steam room

Latin does not need to repeat vapor the second time, because it is understood as the subject of both subordinate verbs.

Abest is from absum, abesse, which literally means to be away from or to be absent.

But in this expression it becomes part of an idiom:

• tantum abest ut ...
  = it is so far from being the case that ...

So you should not take abest too literally here as simple physical absence. It is part of a fixed expression meaning something like:

• it is far from true that ...
• not only does X not happen, but the opposite happens

Also, Latin often uses abest here impersonally. English would usually supply it: it is far from the case that...

Maneat is:

• 3rd person singular
• present subjunctive
• active
• from maneo, manere

Its basic meaning is remain, stay, or continue in a place.

It is singular because its subject, vapor, is singular.

Pervagetur is from pervagor, pervagari, a deponent verb.

That means:

• it has passive-looking forms
• but an active meaning

So although pervagetur looks passive, it means something active like:

• spreads about
• wanders through
• ranges through

Its full parsing is:

• 3rd person singular
• present subjunctive
• deponent

So it means he/she/it may spread through or, in context here, simply it spreads through.

Laconicum is accusative singular, because it follows per, which takes the accusative.

So:

• per laconicum = through the laconicum

A laconicum is a Roman hot-air or sweating room, something like a steam room or sweat bath chamber.

So grammatically:

• per = through
• laconicum = the room being moved through

Because Latin word order is much freer than English word order.

The placement here helps the sentence flow and keeps vapor prominent as the subject of both actions:

• not that the steam stays
• but that it spreads through the room

Latin often places a noun where it is most rhetorically effective rather than where English would expect it. So the position of vapor does not change its function: it is still the nominative subject.

Yes, that is a helpful way to think about it.

The second part, ut per laconicum pervagetur, works much like a result clause after tantum:

• so much / to such an extent ... that ...

But because the whole sentence is inside the idiom tantum abest ut ... ut ..., the effect is stronger than an ordinary result clause. It means not just so much that, but rather:

• so far from the steam remaining, it actually spreads through the whole steam room

So calling it a result clause is useful, as long as you remember that the whole pattern is a special idiomatic expression.

A good paraphrase is:

• Far from remaining in one place, the steam spreads through the steam room.

Or even:

• The steam does anything but stay still; it spreads throughout the room.

That captures the force of the Latin much better than a stiff word-for-word rendering. The key idea is the contrast:

• not this
• but rather that