The logistics are covered by a mixture of Amazon FBA (USA/Canada) and a Chinese 3PL company (all other countries). The only orders I handle myself are the Aussie ones, as well as large orders to overseas universities.
I try to keep at least 6 months' work of stock at any time spread across multiple locations. Given the way social media and online communities work, sales tend to be very bursty. When it got on Hackaday, for example, I sold something like $12k worth in a weekend.
I did run into issues at the start of COVID, as American universities would place huge orders or ask 100+ students to do it individually, but we're now robust to this too!
In terms of manufacturing, this is also outsourced. Full PCBAs are made by a group in Shenzhen. The only work done in-house is packaging them. Combined with the above, this makes the chain immune from the Slashdot effect. If (when) we go viral, I just fulfil every order remotely and then replenish the stock with a large order.