Automatic discounts may be too complex to be shown on the product page.
Say they may depend on what else is in your cart or total cart value.
Other discounts may also apply, etc.
That’s why there is no built-in mechanism to show automatic discounts on product page.
Changing compare_at_price may be not that problematic. CSV export -> Google Sheets with formula to update price -> export to CSV and import to Shopify either natively, or by using an app like Matrixify to do that.
Alternatively, there is a bunch of apps which can update your prices. Mostly paid, but there is a free Flow app which can do that too.
If your discount is simple, like "25% off everything" an option is to use "Custom liquid" section on the product page to display calculated discounted price with words like "Buy this for $XX" or similar...
Note that even Amazon uses "See discounted price in checkout" approach ...