What was the first BIP9 block? Block 370,434 (0x20000007) or Block 398,364 (0x30000000)? Block 370,434 (00100000000000000000000000000111) and (0x20000007)

Yes: BIP9 says set top 3 bits to 001.
No: BIP101 explicitly says set first, second, third and 30th bits to 1.
No: No mention of BIP9 anywhere in BIP101.
No: BIP9 was published after this block.

Block 398,364 (00110000000000000000000000000000) and (0x30000000)

Yes: This is definitely compatible with BIP9, but not explicitly BIP9. It is mentioned in BIP109.
In my opinion block 398364 is the first BIP9 block.
Block 370434 was signaling BIP101. As you say, BIP9 was not created at the moment and even if is was meant to signal BIP9, it would also signal csv and segwit which where not active at the time: https://github.com/bitcoin/bips/blob/master/bip-0009/assignments.mediawiki
Block 398364 uses a BIP9 format to signal BIP109. The 4th bit is used to indicate the block version, 0b00110000000000000000000000000000 (0x30000000) which is within the defined version range of BIP9. But other proposals used the last bits in the version number.
Block 407021 is the first block with version number 0b00100000000000000000000000000000 (0x20000000) so a clear vote for only BIP9.
The green line below shows the BIP109 blocks and blue line BIP9.