Learn Hardcore Russian: Мне стоит убрать телефон, чтобы не отвлекаться на чат. - It’s worth putting my phone away so I don’t get distracted by the chat.

Мне is the dative form of я (to me / for me). In Russian, feelings, necessity, advice, and “it would be good for me to…” ideas are often expressed with a dative experiencer rather than a nominative subject.
So Мне стоит… literally means something like It is worth (it) for me to…, i.e. I should / It would be a good idea for me to….

What does стоит mean here, and is it related to стоить (“to cost”)?

Yes—this is the verb стоить. Besides to cost, it also has the meaning to be worth (doing).
Pattern: (кому) стоит + infinitive = someone should / it’s worth for someone to…
So Мне стоит убрать… = I should put away… / It’s worth it for me to put away….

Is Мне стоит… strong like I must, or softer like I should?

It’s usually softer than “must”. It sounds like good advice or a personal conclusion: I should / It’d be a good idea / I’d better.
If you want stronger obligation, you’d more often use мне надо / мне нужно / мне придется.

Why is убрать used instead of убирать?

Убрать is perfective, focusing on a single completed action: to put away / remove (once).
Убирать is imperfective, emphasizing a process, repetition, or general habit. In advice about doing something once right now, убрать is the natural choice.

What exactly does убрать телефон mean—“delete the phone”?

No. Убрать телефон typically means to put the phone away (e.g., in a pocket, bag, drawer) or to remove it from your workspace so it’s not in front of you. It doesn’t imply deleting anything.

Why is телефон in the accusative case here?

Because убрать takes a direct object: you are “removing/putting away” the phone. For an inanimate masculine noun like телефон, the accusative form is the same as the nominative: телефон.

What does чтобы do in this sentence?

Чтобы introduces a purpose clause: in order to / so that.
Here, чтобы не отвлекаться… means so that I don’t get distracted… (purpose: preventing distraction).

Why is не placed before отвлекаться?

Because не negates the verb: не отвлекаться = not to get distracted.
With чтобы, Russian often uses не + infinitive to express the purpose of avoiding something: so as not to…

Why is отвлекаться reflexive, and what’s the difference from отвлекать?

отвлекать (кого-то) = to distract someone (you distract another person).
отвлекаться = to get distracted / to be distracted (the subject is the one losing focus).

Here you mean I don’t want to get distracted, so отвлекаться is correct.

Why is it отвлекаться на чат—why на, and why чат?

The construction отвлекаться на + accusative is common and means to get distracted by / onto (something)—your attention shifts onto that thing.
чат is masculine inanimate; in the accusative it stays чат.

Could you also say отвлекаться от чата? What’s the difference?

Yes, but it changes the perspective:

отвлекаться на чат = your attention gets pulled to the chat (chat is the distracting target).
отвлекаться от чата = you get distracted away from the chat (chat is what you stop focusing on).

In your sentence, you mean the chat distracts you, so на чат fits.

What word order variations are possible, and would they change the meaning?

Several are possible with small emphasis changes:

Мне стоит убрать телефон, чтобы не отвлекаться на чат. (neutral)
Чтобы не отвлекаться на чат, мне стоит убрать телефон. (emphasizes the purpose first)
Мне стоит телефон убрать… (more colloquial emphasis on телефон)

The core meaning stays the same; word order mainly affects focus and style.