Я чуть не забыл зарядку дома, но вернулся за зарядкой.

Чуть не + past tense is a fixed pattern meaning almost (something happened, but in the end it didn’t).
So Я чуть не забыл = I almost forgot.
The не is part of the construction: grammatically it looks like negation (didn’t forget), but the whole phrase means came close to forgetting.

Забыть / забыл (perfective) is used for a single completed event (or a near-event with чуть не): one moment where you nearly forgot.
Забывать / забывал (imperfective) would suggest a habit/repeated situation or a process (e.g., I used to forget, I was forgetting), which doesn’t fit as well here.

Дома is an adverb meaning at home. Historically it relates to the genitive form, but in modern Russian you can treat дома as a set adverb (like внутри, снаружи).
So забыл зарядку дома = forgot the charger at home.

Зарядку is accusative singular (direct object) of зарядка.
The verb забыть takes a direct object in the accusative: забыть (что?) зарядку.

Because вернуться за чем-то is a common pattern meaning to go back for something.
The preposition за in this meaning requires the instrumental case:
за зарядкой = instrumental singular of зарядка.

No. За can take:

• Instrumental: location/being behind something (за домом = behind the house) and also the purpose meaning go for / return for (вернуться за зарядкой).
• Accusative: movement to a position behind something (за дом = to behind the house), and some time expressions (за неделю = in a week / over a week).

Here it’s the return for meaning → instrumental.

Yes, it can be omitted if the context is clear:
Чуть не забыл зарядку дома, но вернулся за зарядкой.
Russian often drops subject pronouns because the verb ending already shows the person (забыл = I/he; context clarifies). Including Я can add emphasis or clarity.

Но means but, introducing a contrast: almost forgot it, but went back for it.
The comma is normally required because it joins two parts of a compound sentence:
..., но ...

Word order is flexible. You can move pieces for emphasis:

• Я чуть не забыл зарядку дома (neutral)
• Я дома чуть не забыл зарядку (emphasizes at home)
• Зарядку я чуть не забыл дома (emphasizes the charger)

The meaning stays basically the same; the focus changes.

Зарядка can mean: 1) charger (very common in modern speech): зарядка для телефона
2) (morning) exercises / warm-up: делать зарядку

In this sentence, вернулся за зарядкой strongly suggests a physical object you can go back for, so it’s understood as a charger (unless the context is specifically about workouts).

Common options:

• зарядку для телефона = a phone charger
• зарядку от ноутбука = the laptop charger (the one that belongs to the laptop)
• кабель и зарядку = the cable and the charger
  You can still say: вернулся за зарядкой для телефона (instrumental stays on зарядкой).

Yes. Two common alternatives:

• ... но вернулся за ней. (uses the pronoun ней = instrumental of она, referring to зарядка)
• ... но съездил/сходил за зарядкой. = went (by transport/on foot) to get it

Вернулся за зарядкой specifically emphasizes returning to the place you came from.