Okay, this is from memory so take it as something to look into, not absolute.
1. If you move permanently in July 2021, then you become resident as you cross the border. Your tax return looks like 6+ months US resident (filed in US), 6- months Cdn Resident (filed in Canada), 6- months us citizen with world wide income (filed in the US).
2. I would not do the roll over in 2021, I personally would wait for 2022, if ever.
3. Because it is in a recognized by tax-treaty retirement account (IRA, ROTH, 401k), you are not taxed on it until you take distributions.
If taken as regular distributions (Pension-like)
4. The US will take assumed taxes when you withdraw. You will declare that income on your cdn return, and then also declare "foreign taxes paid" which will subtract from what you owe to Canada taxes.
If it is rolled over at one go
You can do a one-time roll over from an IRA to an RRSP after moving to Canada (401k was not recognized officially in the tax treaty so putting it into an IRA is recommended before you move out of the USA).
so, in 2022 you can do the official roll over to Canadian RRSP, When this happens, the US claims standard withholding tax and may also claim the 10% early penalty (doesn't always happen). In Canada you file taxes as above, including claiming all of this income and all the IRS taxes and penalty as "foreign taxes paid". You get a deduct on your tax return for the foreign taxes paid.
Challenge - for some reason CRA limited my IRA roll over to $275k into my RRSP Not sure why, not written out specifically in tax treaty but maybe this was the limit they thought possible to accumulate in a pension account in 3 years US employment... note I rolled over after 6 years in Canada so it grew even larger, so maybe that was it, IDK.
Challenge - To roll over into the RRSP, you need to come up with the cash to make up for the withheld taxes and penalties, immediately, to put the full amount withdrawn into the RRSP account or else you get hit with CDN taxes on the difference (which is in the hands of the IRS).
Challenge - to get full credit for the foreign taxes paid, you need a fairly high income year -- you need lots of Cdn taxes on the return to subtract the foreign taxes from, you won't get $$ back in Canada that were claimed by the USA and no carry over to the next year.. AND the calculation can be a bit tricky, but assume that you need 1.5x in Canadian taxes owed versus the foreign tax credit to make it work.
Roth -- I don't know about this one. I think you just need to keep it in the USA and withdraw it as you like, because it is tax / penalty free and you don't pay tax on its growth in Canada. Check - I really forget the specifics on a ROTH because I collapsed mine before moving.
I did not roll over to ROTH, I went from 401K to traditional IRA before I moved to do the roll over after I moved. Obviously moving $$ into a Roth (ladder, other means) is always a great idea, especially for FIRE.
Yes, having everything in a Roth is a great alternative to this roll over business. I don't think that you would have any tax worries in a Roth and you can keep it as a ROTH in the USA if your US bank allows Cdn Residents to keep US brokerage accounts (only a small few do this).