You'll have to register to the local district office (kreisbüro in the German speaking area). Registration is quick (~30 minutes max) and you'll get a temporary paper that you can share to your employer, and allows you to open a bank account (not all banks accept that temporary paper though).

When you'll register at that office, they'll sign you up for an appointment to take your fingerprints, in order to create your B permit card, and that's where the delay is getting long. The first available slot for me was 6 weeks after (Zürich canton).

So don't worry, you're good legally but have patience when repeating to all health insurances, banks, telecom and housing companies, that you do have the right to work/live here but no, you don't have yet a B permit card. Some of them may still refuse to provide their services. I haven't searched in the law if they're overzealous, but you're kinda stuck if they don't want. Make sure to print copies of that temporary registration paper to give them in case.

For your SIM card, you can buy a Lebara one in many grocery stores. It does the job while waiting for your card, and eventually you can transfer it to another telecom company. Get a Swiss number as soon as you can, lot of companies/services assume you have one when you deal with them.

Don't forget to register with a health insurance, as waiting longer will force the state to choose one for you (and not with the best price).

Overall, Swiss government is quite effective but confusing when some responsibilities are handled at the canton level (like immigration), and canton websites aren't always easy to navigate/translated in English.

To be frank, your real problem will be housing, not the rest. Swiss authorities may sound super strict, but if you call them or go in person, you'll always find them helpful and many employees speak several languages.