Why would 6 stops on a Shimano shifter travel 7 cogs with a Shimano derailleur?

Sounds like you bought the wrong shifter. The "ST-EF500" is available in both 7 speed and 8 speed

A 7 speed shifter has 7 resting positions, and will click 6 times across its range.
ST-EF500-7R4A

Likewise, an 8 speed shifter will click 7 times.
ST-EF500-8R4A

If your cassette has 8 cogs total, then you need an 8 speed shifter.

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If you're totally stuck with these parts, you could make them work somewhat by ignoring one outside cog. The inter-gear spacing between 6/7/8 speed is the same, and the cassette gets wider as gear count increases.

Conversely, 8/9/10 speed cassettes are all the same width, but the inter-cog spacing decreases.

You could choose to disregard either the top or bottom gear, and index the other seven. If you never spin out while riding, then exclude the smallest cog. If you never ride up hills and need a low gear, then exclude the largest cog from indexing.

This is not an ideal solution - the correct shifter would be best.

The only thing I can think of is that maybe the various adjustments are set so initially you are barely on the 8 side of gear 7/8 and after 6 steps you are barely on the 1 side of gear 1/2. It's worth examining your rear derailleur closely to make sure the hanger is straight and the derailleur itself isn't binding or damaged.

I would go through the full recommended setup steps for both the shifter and rear derailleur from the beginning, after making sure that all cable/stop junctions are fully seated, any cable "adjuster is initially tightened to the point where it is 1 turn loose of the fully-tightened state.", the cable loops up front aren't binding when the handlebars are turned full left or right, etc.

Here's the link to the "dealer" installation manual for your shifter/brake lever combo: https://si.shimano.com/api/publish/storage/pdf/en/dm/MBST001/DM-MBST001-01-ENG.pdf

Have you checked that your derailleur hanger is straight? You’d need a hanger alignment gauge like the Park DAG or Shimano TL-RD11, etc. there are lots of different options from different bike tool suppliers, but it’s always my first step with any rear derailleur adjustment, to check the hanger. I also find most of the bikes I see are at least a little bit off. If the hanger is bent inwards, that could cause 7 (or even fewer) gears on an 8 speed shifter to cover an entire 8 speed cassette.

If you don’t have a derailleur hanger tool and don’t want to buy one, you could have a local shop straighten it, use one at a local bike co-op, or, if you have a good relationship with your bike shop of choice, you might be able to borrow theirs if they have an extra one or an empty stand when they’re not busy. I did that once at a bike shop near my college campus (straighten the hanger at the shop, finish the adjustments at home), but that was before COVID.

If you don’t know what you’re doing, you could ask the shop to only check the hanger alignment, and then go through the rest of the adjustment steps yourself. You will have to re-check the rest of your derailleur adjustment after straightening the hanger.