https://metalitalia.com/articolo/bruce-dickinson-il-nuovo-album-the-mandrake-project-traccia-per-traccia/Italian track by track, if you trust Google Translate.
In very, very short:
01. AFTERGLOW OF RAGNAROK
Not representative of the whole album 'cause the album is varied.
02. MANY DOORS TO HELL
Standard simple song, hammond organ, melodic.
03. RAIN ON THE GRAVES
Not among the best of the album.
04. RESURRECTION MAN
Western atmosphere, acoustic guitar, Morricone feel, then the electric part comes in, nice chorus, then it changes mood and goes into Sabbath territory.
05. FINGERS IN THE WOUNDS
Keyboard led, there's piano and acoustic guitars, but it's not really a ballad, some arab-ey melodies and there's a good solo in the Kashmir, Gates of Babylon vein.
06. ETERNITY HAS FAILED
It's just the demo for If Eternity Should Fail.
07. MISTRESS OF MERCY
The most "Accident of Birth" track, '90s feel. Title track, Road to Hell and Starchildren are mentioned for reference.
08. FACE IN THE MIRROR
The first "true" ballad, simple but poignant.
09. SHADOW OF THE GODS
Structured like Omega in the sense that the first half is a (piano) ballad, then it gets heavier. It's a progression - starts acoustic, then orchestral, and then the heaviness arrives.
10. SONATA (IMMORTAL BELOVED)
Described as very experimental, dreamy, a bit of a WTF song that didn't fully convince the reviewer, the more it goes on, the more it goes off the tangent and off the "classic song structure", giving the impression that Bruce is just randomly improvizing vocal lines like if the song was an embryonic one. Totally did not expect such a description.