If you read my answer to that other question you cited and read the National Electrical Code carefully, you will see that your case was NOT necessarily a Code violation.
There is an exception that allows line to neutral loads and line to line loads on the same Multi-Wire Branch Circuit as long as the circuit breaker opens all ungrounded conductors. A double pole breaker satisfies this requirement.
210.4 (C) Line-to-Neutral Loads. Multiwire branch circuits shall supply only line-to-neutral loads.
Exception No. 1: A multiwire branch circuit that supplies only one utilization equipment.
Exception No. 2: Where all ungrounded conductors of the multiwire branch circuit are opened simultaneously by the branch-circuit overcurrent device.
However, single pole breakers with a handle tie do NOT satisfy this other section of the Code.
240.15 Ungrounded Conductors.
(B) Circuit Breaker as Overcurrent Device. Circuit breakers shall open all ungrounded conductors of the circuit both manually and automatically unless otherwise permitted in 240.15(B)(1), (B)(2), (B)(3), and (B)(4).
(1) Multiwire Branch Circuits. Individual single-pole circuit breakers, with identified handle ties, shall be permitted as the protection for each ungrounded conductor of multiwire branch circuits that serve only single-phase line-to-neutral loads.
Additionally, you stated the previous owner continued the 120 volt circuit
for the rest of the garage.
There is a Code requirement that prohibits the garage circuit from supplying outlets outside the garage. Since you stated the rest of the garage I concluded your dryer was installed in the garage. Therefore you could use the double-pole breaker exception cited above.
I would agree it is better form to have those circuits separated but the Code allows it if someone so chooses.
Hopefully, this post helps advance the understanding of this particular section of the Code.