zombiequeen66's journey

I had my final interview yesterday for a PRN social services role, and it went really well. At the end of the interview, the HR officer expressed that they would love to have me on the team. Later that day, the hiring manager even texted me to ask for my preferred start date and availability for training. I mentioned an end of June start date, and she seemed pleased with that, saying she would prepare a training schedule to send me at the beginning of next week. However, I'm feeling a bit anxious because I haven't received any formal offer letter, background check request, or onboarding paperwork yet. Is this a normal timeline? I’m wondering when I should start following up if I don’t hear back soon. On top of that, I currently work full-time and might need to transition to PRN if I accept this new role. Should I wait for the onboarding paperwork before discussing this change with my current employer, or does the communication I've received so far seem solid enough to start planning my next steps?