Hi,
HikaAuction already displays this: on the auction page, logged-in bidders get a "Your max bid" line in the auction details, showing their current maximum bid (€ 100.000 in your example), and it is refreshed by the live updates. Since the texts on your page ("You are leading the auction", "Place live bid for") are not the default HikaAuction ones, I suppose you have a template override of the show_auction view, and that line may have been removed or hidden in it. Could you check if you see it with the default template ?
If you want to add the explanation about the price paid, you can change the text of that line with a language override of the key HKA_YOUR_PREVIOUS_MAX_BID in System > Language Overrides, for example: Your max bid (if you win, you only pay the second-highest bid plus the bid increment)
About the button, you're right that it is confusing: when the leading bidder has a max bid above the current price, the button offers a bid of their max bid plus the increment, so each click raises their own max bid. We're thinking about changing this so that, for the leading bidder, the page shows the "you are winning" message with their max bid and the explanation above, and replaces the bid button with a "Raise my max bid" field instead. Would that work for you ?