Re: "Last Seen"
It seems like you guys are in the second phase of the relationship where all the excitement of getting to know a person goes away and you just have personality/similar hobbies that are left.
The second part of the problem is it seems you guys are in a LDR which kind of makes the situation worse. Both sides have to put in a equal amount of effort, and it seems like you are doing your part but she's not doing hers.
So, you have a couple of options here op...
The first one is say no to your parents, which obviously you are scared/not sure of doing. And cancel the engagement. With how things are going this is probably the best scenario. I would bring this up with her first, tell her straight up, "I feel like I'm always the one trying in this relationship, and you need to also put in the same effort other wise I don't think this will work and I will call off the engagement"
Like a person can be busy, but it doesn't take a long to respond with, "sorry I'm busy will text later. "
But I also suggest you tell her to go into her stupid whatsapp options and turn "last seen off", it seems like you are always in your own mind, and if you don't see her last seen, it will take some tension off of you. Out of sight..out of mind,
The second is... and I don't recommend this, but it does have its place... is to play her stupid game. Ignore her, let her initiate. While you go find another girl to talk too. If she has another secret boyfriend, fine..let him have her. If you've already talked to her about not putting in the same effort as you in the relationship than, I would start moving on to greener pastures while stringing her along as she is stringing you along. As other posters have suggested, the evidence kind of points in this direction. You can't 100% know she's talking to another guy, but this helps you double down and minimizes risk.
How many potential risthas have you talked to before meeting her? Just interested in knowing.
The third is to just suck it up and wait, if you like the way she looks, her personality, her hobbies and interests than wait until the wedding, go find a hobby and let her do her own thing. Go watch some tv shows, go learn a new language. Keep your self busy without her in your life. As it always has been.
If you feel you can do better, than go to option 1.
But the way I currently see it, it seems talking to this girl and checking her last seen on whatsapp has become your new hobby. But you guys are engaged, one would normally assume you guys are exclusive and I don't think she'll be talking to another guy, especially if she traditional/conservative as you say. Maybe you guys have run out of things to talk about? If im on the phone with a girl, I'm usually talking to her for 30+ to 1 hour each time.
Hope this post gave you some insight. sorry for the length