I'm getting an error message saying I have formulas exceeding 8192 characters. How do I get rid of this error message?

Make the formula shorter!

In Excel, 8192 is maximum number of characters the formula can be composed of (google for "Excel specifications and limits" for more info).

Ways to get shorter formulas:
1. Try to avoid using spaces in your formula whenever it's possible;
2. Use defined Tables, and Table formula syntax, with keeping Table and column names as short as possible (e.g. you can get the formula in format like =SUM(tbl1.[fld1]) much shorter as the same formula in format =SUM(Sheetname!$AAA$2:$AAA$9999);
3. Use helper columns to get intermediate results for your formula, and refer to them further instead writing the whole formula into single cell;
4. Use [dynamic] names as intermediate sources for your formula.

Having a good night of sleep, I can continue...
5. Use better design of your workbook. Usually having such long formulas is a sure indicator of poor design! Mostly this is caused by entries of same type divided between many worksheets, or many columns. E.g. you have an Excel app where you enter purchase info. Often users design this exactly in same way, like someone in year 1700+ in some paper notebook, e.g. separate columns for different purchased articles in same table, or separate tables (i.e. data on separate sheets in your excel) for different suppliers, or for purchases in different months, etc. This means you get very long and unhandly formulas whenewer there will be need to calculate any totals. An additional downside is, you have to redesign your workbook, whenever a new month is starting, or when a new supplier must be added, etc. When you keep all this info in single table, a single column for every type of data, all such calculations are reduced to using simple SUM(), COUNT(), SUMIFS() and COUNTIFS() formulas. And in case you really need to visually present e.g. data for single supplier, or single month, or single year, you create report sheets (a single report sheet for certain conditions set, e.g. a single Monthly report), where you select report conditions, and report table reads info matching those conditions from data entry table. With such design, you can use your workbook for years without any need for any redesign!

Re #4: I make extensive use of helper columns. Some of my workbooks have entire "helper sheets" that stay hidden.

Another idea for shortening formulas: If there are a bunch of repetitive parts, you might be able to make use of the =LET() function.

Why not post your formula ( or part of it ) so we can see what seems to be the problem ?
@Steve
As the OP's profile indicates he is using XL 2019 the LET function is not available (and your profile states the same?)

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Good catch -- I didn't notice that.
And thanks for the prompt -- I'll update my profile!

I changed it to "2021" but my Excel actually shows "365."

Good catch. it seems 365 is not available in the User CP. I'll contact a mod about that

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