The argument against publishing prices is that it invites comparison and loses people who would have been persuaded in conversation. Both are partly true and both understate the cost of silence. A visitor who cannot find any indication of price assumes the worst, and the ones who leave are frequently the ones who could have afforded you but were not willing to book a call to find out.
Publishing also filters, which is the underrated benefit. Every conversation you do not have with somebody whose budget is a fraction of your price is time returned. For a business of one, that filtering is worth more than the occasional prospect who might have been talked upward.
Where a fixed price is genuinely impossible, publish something rather than nothing. A starting figure, a typical range for the work you most often do, or an explanation of what moves the number up and down. Projects like this typically run between one figure and another, and what determines where you fall is these three things, is considerably more useful than requesting a quote, and it does most of the same work as an exact price.
Be careful with the lowest number if you use a range. Readers anchor on it, and a range beginning at a figure you rarely charge produces disappointment in every subsequent conversation. Set the bottom of the range at something you would actually accept.
Include what is not included, because that prevents the most common misunderstanding. Somebody comparing your figure against a competitor's is usually comparing different scopes, and stating the boundary makes the comparison honest rather than leaving them to assume.
If you decide against publishing, at least explain why on the page where the price would be. A sentence saying that the work varies enough that a number would mislead, followed by what determines it and how to get a real figure quickly, respects the question rather than ignoring it.
Whatever you publish, review it whenever your prices change rather than annually. A pricing page showing figures you no longer charge is worse than none, because a prospect arrives anchored to a number you have to correct in the first conversation, which starts the relationship with a disappointment you created.