re: Employer Offering Roth 401K

I think you are stating the plan backwards.

I split my contributions in both, with the thinking that I’d pull from my Roth in years where I make big purchases and pull more Roth money in December to fund living expenses for the following year. The next year, I’ll only pull traditional money to remain in the lower tax brackets.

Am I thinking of this the correct way?
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More to it than that. It depends on your income each year when pulling out money. Pull from Roth in years you are trying to stay out of the tax brackets that have the larger jumps. The tax brackets are not evenly formed. Some have 10% jumps between rates and some have 2% jumps.

2023 Federal Income Tax Brackets Married Couples Filing Jointly
Tax Rate For Married Individuals Filing Joint Returns
10% $0 to $22,000
12% $22,000 to $89,450
22% $89,450 to $190,750
24% $190,750 to $364,200
32% $364,200 to $462,50
35% $462,500 to $693,750
37% $693,750 or more

You should try to keep money out of the ranges where the taxable jumps the most, which is from 24% to 32%, and from 12% to 22%. So, when income gets above $364k, it is taxed at 32% instead of 24%. Although it is only the marginal amount above $364k and not the entire amount.

Since Roth money was already taxed when you put it in, you only owe capital gains on that income, and not the amount you contributed. The traditional were not taxed when you put it in, and now have federal and state tax owed when you withdraw. This tax rate is generally higher than the capital gains rate, which is either 15 or 20%. But the gains on your Roth money could be significantly more than your gains from your traditional depending on how you invested into each, so it can be complicated. The best way to know where to pull money from is to plug in scenarios into tax software to compare each.