That's now how dividend taxation works. Most people do not seem to get it. Here is how I try to explain it to people. This is simplified to the extreme, standard deduction only, etc.
Imagine that you have a glass cylinder with lines drawn on one side representing the tax brackets on ordinary income (salary, interest, pensions, Roth conversions, distributions from deductible traditional IRAs, etc. Really, everything EXCEPT qualified dividends and long-term cap gains.). For a single in 2020, income is not taxed below the standard deduction amount of $12K. Ordinary income between the lines for $12K and $22K is taxed at 10%. Between $22K to $52K, 12%. Between $52K to $97K, 22%. Etc. Pour all your ordinary income into the cylinder, let's imagine that it's red sand. Add up the taxes on that income. That is the tax on your ordinary income and nothing you do can change it. Every incremental dollar of ordinary income is taxes at its level in the cylinder.
Now turn the cylinder around. On the other side are a second set of lines for the tax brackets on qualified income (qualified dividends and long-term cap gains). For a single in 2020, the rates are 0% below $52K, and 15% above $52K. (Also a 20% CG rate up near half-a-mil.) Pour your qualified income into the cylinder with a blue sand. It sits ON TOP OF your ordinary income. Calculate the tax on the qualified income, based on where the blue sand sits in the cylinder.
Your total tax is the tax on the red sand using the ordinary bracket rates, plus the tax on the blue sand using the qualified rates. The dividend income CANNOT affect the tax on the ordinary income. Really, it's the other way around since again the blue (qualified) sand sits on top of the red (ordinary) sand.
If that analogy makes sense, I hope you can see that dividends cannot "push you over a bracket". That's just NOT how it works.
I do not mean to argue for or against dividends, although I very very strongly believe in them as the foundation of my retirement income. Understanding how taxes work is crucial.