At $200k/year income you're not deferring taxes!
With the 401(k) and your income, you are not eligible to deduct your contribution to a traditional IRA.
What you are actually creating is a Non-Deductible IRA (NDIRA). That's not a third kind of IRA, merely a treatment of a traditional IRA.
You will not be taxed twice. You won't owe more tax on the amount of your contribution to an NDIRA, however, the appreciation will be taxed. So for instance if you invest $5000 and have earned $45,000 in gains by retirement, you will only pay tax on 90% of the money. *Remember this point, as we're about to take a turn into "super stupid".
Your best bet is to do a Roth Conversion of the NDIRA. Normally you need to pay income tax on a Roth conversion. But since you already paid tax on the principal, you'd only need to pay tax on any appreciation, e.g. $300 gains so far.
So you might as well be in a Roth.
In a Roth, appreciation is not taxed. And since you already paid tax on Roth contributions, those aren't taxed (again). So if you invest $5000 and in retirement it's had $45,000 gains, you only pay tax on NOTHIN'!
NDIRA: principal not taxed again. Gains taxed.
Roth conversion: Principal not taxed again. Gains not taxed EVER.
Cost to convert NDIRA to Roth: next to nothing.
Converting your NDIRA to a Roth is the very definition of a "no-brainer" lol.
This whole thing is called the Roth Backdoor, and was specifically authorized by Congress. For tax advisors, there was some uncertainty on this point, since it was done with virtually no recorded documentation other than the law itself. However in later years, both Congress and IRS mentioned it in passing in documentation, and so it is clear both consider it to be law.