Learn Hardcore Japanese: nimotu ga omosugite, hitori de ha hakobemasen. - The luggage is too heavy, so I cannot carry it by myself.

The て-form here expresses a cause–result relationship in a neutral or conversational style:
“(Because it’s too heavy,) I can’t carry it alone.”
You could also say:

荷物が重すぎるので、一人では運べません。
荷物が重すぎるから、一人では運べません。
But 重すぎて is more direct and common in spoken Japanese.

What’s the function of は in 一人では運べません? How is it different from just 一人で?

一人で means “by oneself.” Adding は—一人では—marks that entire phrase as the topic or point of contrast:
“As for doing it alone, (it) can’t be done.”
It emphasizes that, at least when you’re alone, carrying it is impossible.

Why is it 運べません instead of 運びません?

運べません is the negative potential form, “cannot carry.”

運ぶ (to carry) → potential 運べる (can carry) → polite negative 運べません (cannot carry).
By contrast, 運びません simply means “do not carry,” without implying inability.

How do you form the potential form 運べる for a verb like 運ぶ?

運ぶ is a Group 1 (u-verb). To form the potential:

Change the final -u sound to the corresponding -e sound: 運ぶ → 運べ
Add る: 運べる (can carry)
For the polite negative: drop る and add ません → 運べません.

Can this sentence be rephrased more formally or with different connectors?

Yes. For more formality you can use ～ことができません:

荷物が重すぎて、一人では運ぶことができません。
Or replace the て-form with ので/から for a slightly different tone:
荷物が重すぎるので、一人では運べません。
荷物が重すぎるから、一人では運べません。