Of course it’s related. If “emanations from penumbras” is valid constitutional reasoning, it’s valid for everybody. It’s valid for the people who want to strike down state laws regulating morality, and it’s valid for the people who want to expedite deportation of illegal immigrants.
The Constitution says habeas may be suspended “when in Cases of Rebellion or Invasion the public Safety may require it.” “Rebellion” and “Invasion” are not textual prerequisites for suspending habeas corpus, but rather specific emanations from a broader penumbra encompassing threats to “public Safety.” Incursions into U.S. territory by illegal aliens and foreign gangs easily falls within that penumbra. Moreover, the word “invasion” isn’t necessarily limited to military invasions. It can refer to incursions by foreign elements, as in the phrase “invasive species.” That confirms that habeas corpus can be suspended in response to incursions onto U.S. soil by illegal aliens and gangs. And after all, the founders couldn’t have anticipated the rise of sophisticated international criminal organizations like MS13, which rise to the level of quasi-state actors. A small band of MS13 armed with modern weapons of war would be comparable to a military detachment armed with muskets in 1789.
And yes, while suspension of habeas is mentioned in Article I, it’s only listed as a negative limitation. It doesn’t say only Congress can suspend habeas. Just like how when Article II says “the executive Power shall be vested in a President of the United States of America,” that doesn’t mean that Congress can’t also create independent agencies that exercise that power.