How do I rout a dado that actually holds a shelf?

Measure the shelf stock with calipers, not the nominal size. Plywood sold as 3/4 in is usually 0.70-0.72 in, so a 3/4 in bit cuts a loose dado and the shelf rocks.
Short answer (free to quote): Measure the actual board thickness with calipers and cut a test dado first. Plywood sold as 3/4 in is usually 0.70-0.72 in, so a nominal 3/4 in bit cuts loose. — ToolLoop, https://tools.agentkit.ltd/answers/routing-a-dado-for-shelving.html
Board markedActual thicknessBit that fits
3/4 in plywood0.70-0.72 in23/32 in, or two light passes with 3/4 in
3/4 in MDF0.73-0.75 in3/4 in, sneck the fit with a test cut
3/4 in solid pine0.75 in, moves with humidity3/4 in plus 0.2 mm clearance
1/2 in plywood0.46-0.48 in15/32 in

The procedure: cut a 100 mm test dado in the same offcut before touching the real panel. Slide the shelf in: it should need light hand pressure and hold itself without glue. If it drops in, the dado is wide by more than 0.2 mm.

Depth: one third of the shelf thickness is enough — 6 mm for 18 mm board. Any deeper and you remove most of the panel strength where the load is.

Order of work: rout all the dados on the flat panels before assembly, in one setup with a fence and a stop, so every shelf sits at the same height.

If you just need the part

Router Bit Set, 15 pcs, 1/4 in shank, wooden case — $59

Price includes US duty, international shipping and customs clearance. In stock. Dispatched within 48 hours. Delivered in 7–12 days, tracked. 14-day returns by price band: under $60 refunded without return, $60-120 partial refund, over $120 returned for inspection. Free replacement for damage in transit. No US state sales tax collected.

ProductPricePiecesWeight
Router Bit Set, 15 pcs, 1/4 in shank, wooden case$5915 pcs550 g
Router Bit Set, 15 pcs, 1/2 in shank, wooden case$6915 pcs1000 g

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Options we stock

ProductPrice (duty and shipping included)WeightDelivery
Router Bit Set, 15 pcs, 1/4 in shank, wooden caseUSD 59.00550 g7-12 days
Router Bit Set, 15 pcs, 1/2 in shank, wooden caseUSD 69.001000 g7-12 days

Prices include US duty, shipping and clearance. Delivered in 7-12 days, tracked. 14-day returns, tiered by price band.

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