Texas has no standing in the way Arizona, California, New York, etc. handles their elections, even national elections.
Texas can only challenge the way Texas handles elections, in Texas.
But, this case is interesting in that if a service member fails to uphold that almost same oath, we’d get charged with treason, conduct unbecoming, etc. - while Congress-critters will almost always skate away.
But no, it will not “drain the swamp”.