Quick answer
Name the action, give a date, and give one link. "Please reply by 14 May" outperforms "kindly respond at your earliest convenience" in every setting, formal ones included.
Formal
The favour of a reply is requested by the fourteenth of May.
Kindly respond by 14 May at [link].
We would be grateful for your reply by 14 May so that we may confirm arrangements.
Warm and modern
Let us know if you can make it by 14 May — it takes about ten seconds: [link]
We would love to know if you can join us. Please reply by 14 May.
Yes or no, both are welcome — just let us know by 14 May.
Casual
Coming? Tap here to let us know by the 14th: [link]
Give us a yes or a no by the 14th so we know how much to order.
Corporate
Please confirm your attendance by 14 May so we can finalise catering and room capacity.
RSVP by 14 May. Places are limited and allocated in order of response.
Please respond by 14 May, including any dietary requirements, using the link below.
Asking for dietary needs
Please tell us about any allergies or dietary requirements when you reply — we will pass them to the kitchen.
Let us know your menu choice and anything we should know about allergies.
Plus-ones, stated clearly
This invitation is for [name] and [partner]. / We have reserved one seat for you and a guest. / We are keeping numbers small, so we have reserved a seat for you.
Reminder wording
Just checking our invitation reached you — replies close on 14 May: [link]
We are finalising numbers this week. If you have not replied yet, here is the link: [link]
What makes any of these work
Three things, in every register: a specific date, a single action, and no ambiguity about who is invited. Elegance is optional; clarity is what produces replies. When each guest receives their own link, the wording can stay short because the system already knows who is answering.