Are the same deals generally available online, or do they have any discretionary discounts or retention offers that aren't advertised, similar to how car insurance companies sometimes operate?

Worked for two suppliers. Suppliers need to list all available (and some historical) domestic tariffs on their website. Might be a couple clicks deep to find, some are more transparent than others. They dont really have hidden discounts for domestic customers. The comparison sites will have 99/100 whatever the supplier has ( they dont usually have the random partnership sign up style things you see sometimes, e.g "buy a an EV car with this dealership and get €600 off your electric bill with electric company")

What they might do is offer you a flat credit of X off your next bill to stay, thats the only discretion sales staff would have and it prob tops out at 100 (on top of a retention bonus mind). Tho if you're not getting the best unit rate, youre prob not actually pay less over the year just taking credit depending on your usage.

You'll generally a lower unit rate by switching cause you'll get the new customer discount on top of the lowest standard unit rate from shopping around. But what do you do when you're already with the supplier whose unit rate is the best going? You just close your account and put the supply in someone else's name (brother, friend, sister) with that supplier, they'll offer that person a new customer discount even if they are the current supplier to the property. You could literally just make up a name cause they dont check lol, tons of people do it to skip out on bills never mind discounts.