TLDR: I got hired by a UK company as their third developer 6 months ago, on a temporary contract. As I am a 'junior' developer, I was offered half of the stated salary, with an email from them saying it would go up should I be offered a permanent role. My temporary contract just came to an end, and they've offered me a permanent role, but without increasing my salary at all.
I've had to accept, as I can't afford to be without a job, but I also can't afford to stay in this role as I end up further into debt each month on what they pay me. My initial mistake was not getting it in writing from the off, that my salary would be increased to £x if I was offered a permanent role.
After being treated this way, why then do I feel a huge amount of guilt that I'm actively soliciting other roles every moment that I'm not at work? Is it normal to feel like I'm going 'behind their backs', so to speak?
In software, you will be able to find a new job easily. Perhaps not the same day, as it occured to my dad in your exact same situation 50 years ago (he just crossed the road and got a better job), but you'll be able to find a new job in less than 2 weeks. So just start looking and interviewing, and when you have a proposal, give your notice.
You can consider the fact that they didn't double your salary as promised as a "polite" way to ask you to leave them.