I'd report given what you describe.
SS aren't the ogres many people on here believe they are. They're not going to swoop in and remove the children. They are there to provide support to families to ensure that children can remain living with them. It's only when parents fail to engage with support services that plans to remove are pursued. The LA does not have the resources to remove children willy nilly and it's not the SW who makes that decision. If they feel it's necessary, they discuss it with their Team Manager and, if they think it's necessary, they compile the evidence to present a case to court and that is where the decision is made.
Exceptions to this are where it is believed the children are at immediate risk of harm, but then it is only temporary.
Parents are supported. That's the whole point of CIN or CP plans etc.
She's got a lot on her hands if she is in her early 20s and has 3 young children. Women who find themselves alone with 3 small children at that age and living in those conditions quite often have unmanaged mental health needs that will only get worse without support/intervention.
SS won't care that the bed has no headboard, but they absolutely will care that there are no sheets on the bed and they will care that there is vermin and no food. The contents of the fridge, the state of the kitchen and bedrooms are things they look at.
SS involvement can lead to other support for her - access to charities that provide other support for example.
If you don't want to get personally involved (and I understand that), then report.
You can contact the NSPCC and explain the sitatuion and seek advice anonymously. That might reassure you.
Please do report it. Safeguarding is everyone's responsibility. Those children deserve a better life than this and their mum is currently struggling to provide it for them, or choosing not too. Either way, it's the children who you should be thinking about, not whether SS involvement would be nice for the mum.