I think it is cool that you are trying to do some recording. I have been doing audio for most of my life, but have never recorded birds. I took your recording into my app for VinylStudio and checked your levels. After setting the volume level by the VU meters, it normalized at -4.4 db. I'm sure VinylStudio is overkill for bird recordings but it works for any audio. I also de-noised the recording.
Don't know if this will play, but here it is.
https://www.youtube.com/watch?v=MF5yaFTZSs0