The likely reason your Square D tandem HOMT2020 breaker doesn't fit in your electrical box load center, is because the HOMT2020 breaker is a CTL breaker (short notch), and your electrical panel (or breaker opening) needs to use NON-CTRL breakers (long notch: 3/4" inch). See here: https://www.se.com/us/en/faqs/FA111464/ Why don't the HOMT tandem breakers fit into all Homeline load centers?
That said, Square D HOMT2020 CTL tandem breakers can fit by dremeling out the plastic rejection tab to make the notch opening longer or 3/4" (this is not recommended for the DIYer), but Home Depot and Lowes seems to only sell the Square D HOMT2020 CTL tandem breakers (short notch). Essentially, you'd dremel out just the plastic to make the notch longer 3/4" (there's a line in the plastic of the breaker around 3/4" , this is where you stop dremelling) .
However, Home Depot / Lowes do seem to sell EATON BR2020 BR 2-20 Amp Single Pole Tandem Non-CTL Circuit Breakers, that have the larger notch 3/4") in the throat of the breaker, but that may still be too short in the bottom part of the breaker to fit completely / connect to the bus bar without dremeling about an 1/8" of an inch of the plastic to make bottom notch sligtly longer, to fit on a Square D / Homeline load center. That said it's not UL listed and Eaton says the BR2020 "is not UL listed to fit in a Sq D panel. You will want to look at our Classified (CL) breakers.
I've seen both the Square D HOMT2020 tandem breakers and Eaton BR2020 tandem breakers fit into a Homeline load center (that only fit) when the plastic notch is dremeled out to make the notch big enough to seat properly. That being said, while EATON breakers may fit in a Square D / Homeline loadcenter, it's better to stick with the recommended breakers for your loadcenter such as Square D and / or siemens.
Siemens CTL tandem 2020 breakers also have a rejection tab, but it is a metal rejection clip. (not sure if this can be removed easily or not). But they do seem to make a NON-CONTROL tandem 2020 breaker without a clip: Q2020NC (no clip) - Siemens 20 Amp Tandem Breaker
Siemens also has a Siemens Q2020NCU (2) 20 Amp Tandem Single Pole Type QT NCL-Circuit Breaker, which Home Depot sells, but it will be more expensive at around $40. This Non-CTL breaker has the larger side notch 3/4", but it has a short bottom notch, so it may need to be dremeled out 1/8" or so on the bottom to sit properly in some Square D / Homeline loadcenters.
NOTE: You should not be dremeling out a tandem breaker if it's not meant for your Electrical panel as this could make the electrical panel / home unsafe.
What is the difference between CTL and non-CTL breakers?
"CTL stands for circuit total limitation. This normally is applied to the "twin" or 2 in 1 breakers used in residential loadcenters. CTL breakers have a rejection feature on the bus connection side of the breaker. This prevents them from being used in certain areas of a loadcenter. Non-CTL breakers do not have this rejection feature and will fit in any space in the loadcenter." - Eaton