Learn Hardcore Chinese: jìshùrényuán yìfāngmiàn jiǎnchá guāngmāo, yìfāngmiàn chóngqǐ lùyóuqì. - On one hand the technician checks the optical modem; on the other hand the technician restarts the router.

Breakdown of jìshùrényuán yìfāngmiàn jiǎnchá guāngmāo, yìfāngmiàn chóngqǐ lùyóuqì.

What does 一方面...一方面... mean here?

It introduces two parallel aspects or actions.

In this sentence, it means that the technical staff are handling the situation in two ways:

A natural English sense is:

It does not always mean a strong contrast. Often it just presents two sides of the same situation.

Is 一方面...一方面... the same as 一边...一边...?

Not exactly.

一边...一边... usually emphasizes doing two actions simultaneously and is common in everyday speech.
一方面...一方面... is a bit more formal and often emphasizes two aspects, two approaches, or two parallel actions.

So in this sentence:

一边检查光猫，一边重启路由器 sounds more like someone is literally doing both at once.
一方面检查光猫，一方面重启路由器 sounds a bit more like two troubleshooting steps being carried out in parallel.

Both can work, but the original sentence sounds more formal and report-like.

Does this sentence mean the actions happen at exactly the same time?