If I'm a senior project manager, should I still keep learning new technology?
For example, every month every year, most language updates themselves, and a lot of new programming concepts become popular. Many new frameworks and patterns are created and make things easily.
If you are a PM (in any sense that I understand them to operate) make sure that you are on top of your game with regards to what you need to do first. This probably involves a lot of client liaison, presentation watching and delivery, requirements gathering, specification consuming, requirements analysis, minute taking, ego massaging, tea making, creating or facilitating the creation of SOWs, making huge Gantt charts is MS Project and working with the team to create project backlogs in Jira. That's quite a lot of work.
You have made it to senior so you probably have some of that nailed. So now you put your other head on (and in some places I think this is probably referred to as Technical Project Manager) and you make sure that you understand, high level, what technologies your team is using and what they can do with them. This gives you confidence, should make your team meetings less bewildering, enables you to engage better in project/sprint planning, allows you to call BS on dodgy developers, stops you selling things that your team cannot build and should increase your gravitas in client meetings when you confidently say yes we can - or, when required, no we cannot. Your knowledge need go no further (for professional reason anyway, you might fancy it for fun), you have a team, presumably with TTLs, TDs and TAs; it's their job to advise you when a new technology has entered the fray. Trust them.
Your role should not require you to learn how to code, but that does not mean not learning new technology. For example you should understand what the latest project management tools bring to the table and how that may improve your project lifecycles. Maybe you don't use any project or bug tracking software, so you learn Jira (easy) and you learn how it fits your organisation, clients and project structure (hard).
Be good at Project Managing, manage the clients expectations, if you don't understand the tech, don't promise that you can deliver something and make sure you've got a pocket developer with you in key client meetings and to proof read your E-Mails.