Angels' spellcasting is not tied to their deity
As quoted in the question, the Monster Manual gives us information about angels. Later on in that same section is a description of the fallen angel - angels which have committed an evil act and become marked as an outcast. The section on fallen angels includes the line:
Fallen angels retain their power but lose their connection to the deities from which they were made. (MM p. 15)
This does not specifically mention alignment changes, but it does say that an angel retains its full power when fallen and disconnected from their deity, and I would expect that to include alignment changes.
Examples from adventure modules
As there does not seem to be much more information to lead us to an answer from the angels' description text, I looked for examples of fallen angels in published works. Here are a couple examples, which I will spoiler-tag since they are NPCs from adventure modules:
Curse of Strahd:
Curse of Strahd includes an NPC called The Abbot, who is a deva that has been corrupted by the Dark Powers in Barovia. The entry for The Abbot includes the following line:
"Statistics. Use the deva stat block in the Monster Manual, but change the Abbot's alignment to lawful evil." (CoS p. 225)
Other than alignment, all the statistics for The Abbot are the same as the Monster Manual deva, including spellcasting.
Waterdeep: Dungeon of the Mad Mage:
Waterdeep: Dungeon of the Mad Mage includes an NPC named Fazrian. Fazrian is a planetar that has become corrupt with power and seeks to destroy any creature it believes is undeserving of continued existence. The entry for Fazrian includes this line:
"Fazrian is a lawful evil planetar that lacks the Healing Touch action option. Unless he is incapacitated, Fazrian can take one of the following lair actions on initiative count 20 (losing initiative ties) while on the Terminus Level..." (WDMM p. 275)
The statistics for Fazrian are mostly the same as a Monster Manual planetar, losing Healing Touch but gaining lair actions, and the spellcasting is exactly the same even with an alignment of lawful evil.
For those that do not want to read the spoilers, both of these are examples of lawful evil fallen angels, which are the same creature type (celestial) as before their fall and contain identical spellcasting capabilities.
Conclusion: angels' spellcasting is not alignment-dependent
Given the description of fallen angels retaining their power from the Monster Manual's description, and the examples above of lawful evil angels using almost all the same statistics (including spellcasting) as their lawful good counterparts, I would conclude that an angel's spellcasting is not dependent on its alignment.