Is domain knowledge more important than BA tools for this switch?
Considerably, and it is where testers have an underrated advantage. Someone who has tested a lending or claims or payments application for years understands the business rules in operational detail. Tooling can be learned in weeks. That is why staying within your existing domain makes this transition far easier than combining a role change with a domain change simultaneously.
Should I move to business analyst or automation instead?
They lead to different careers, so decide on preference rather than on which looks easier. Business analysis moves toward stakeholders, domain depth and eventually product or functional consulting. Automation moves toward engineering depth and pays well within technical tracks. Testers who dislike coding but enjoy the analysis and communication side of defect triage generally find business analysis a better long-term fit.
Do I need a certification to be considered for BA roles?
It is useful mainly for getting past screening when your current title says tester, since automated filters look for the vocabulary. It will not carry an interview. Panels ask how you would handle a stakeholder who keeps changing scope, or how you would document a process nobody has written down. Those answers come from practice and prepared examples, not from a syllabus.
How do I get BA experience while still working as a tester?
Move upstream inside your current project. Join requirement walkthroughs, write the clarification log, volunteer to document an undocumented process, and take the acceptance criteria work nobody wants. This is usually available because teams are short on documentation effort, and it produces exactly the evidence and internal references the transition needs before you go to the external market.