Why not write seedphrase on the booklet (or other paper or not paper only) using ink that can only be seen under certain lighting conditions? For example, ultraviolet.
Invisible inks generally have quite a limited lifespan. Most UV pens will last somewhere around 3-5 years, but it will depend on the type of ink, the type of paper, the conditions of storage (temperature, humidity, etc.), and so on. You might find that the lifespan of UV ink is significantly less than this, and you would have no way of knowing unless you tested it first and waited several years to assess for fade, which obviously no one is going to do. The last thing you want is to come back to seed phrase in a couple of years to recover your coins and find that the ink has degraded so much that you now can't make out all the words.
You can engrave the seed phrases in an aluminum plate as it is resistant from fire and water exposure.
Aluminum is a poor choice for engraving a seed phrase. It has low durability, low strength, low melting point, high malleability, and high reactivity. Probably the best metal to use would be titanium, but the best balance between cost/ease of access and durability is stainless steel.