It sounds like you're doing a good job already. It definitely takes time to understand all the interconnected and complex ways the trans lobby intersects with issues like women's rights, freedom of speech, children's rights and so on. So keep reading the threads here and participating.
No one will ever become an expert in all these issues, but over time you will start to gain a deeper and more well-rounded view.
Your ideas sound like a sensible starting point - create a separate account for social media if you'd like to protect your privacy and keep it separate from your professional and personal life. Follow groups and individuals who are vocal and outspoken on these topics. I find a lot of news gets posted in this forum anyway so it's rare to miss out on what's going on elsewhere.
Donate to crowdfunders if and when you can, write to politicians - even send some of them thank you cards if they seem to be standing up for women's rights. It makes a big difference to receive an actual physical card with a thoughtful message of thanks. The appreciation and support feels more tangible, if that makes sense.
Fill in public consultations, please! They can be tedious and long, but every response helps.
You can speak to family and friends. It doesn't have to be directly about trans issues or confrontational. You can highlight certain problems or conflicts via thoughtful questions. People don't change their mind overnight. It took a while for you of reading and thinking things over before you came to a decision. A lot of people have never given these topics much consideration before. You might find it frustrating that they resort to simplistic answers, but be patient. It can be difficult to connect all the dots. My partner used to think I was being a bit dramatic and conspiracy theory minded when I was initially talking about the erasure of women's rights and the trans lobby. I think seeing the case of Maya Forstater where the fact that there are only two biological sexes (a position held by the vast majority of people including the scientific community) was proclaimed by the judge to be incompatible with society, Harry Miller and the 'non-crime' hate crimes, academics being hounded out or harassed etc have made him a bit more reflective and appreciative of what's at stake here. He's not dismissive of my concerns anymore.
When lockdown eases up, I'd imagine some of the grassroots women's groups might hold public events again. If you can make it along to some of them that would be great. It makes a big difference to meet like-minded people in person. Online interactions are nice, but can still feel isolating at times. You might make friends and know there are others like you in your local area.
You don't have to be an expert to help out in small ways - there might be audio or video clips that need transcribing; long, detailed documents that need reading through to pick out what areas have been captured by the trans lobby - we've seen the good work with parents examining school material and flagging up problematic stuff being taught to their children or policies that contravene the law.
You've done the biggest and hardest step though - reading the evidence and arguments from different sources and making up your mind. A lot of people shy away from engaging as soon as something is labelled 'transphobic' or 'unkind'. You have used your critical thinking skills and looked beyond that to examine the issues for yourself. 