This study uses the normal definition of weaning as the cessation of breastfeeding. It is well known that formula feeding increases the incidence of gastrointestinal infection, asthma, eczema and allergies. This study attempts to elucidate the mechanism of this however it has nothing to do with early introduction of solids
I find it interesting that people are so devoted to six months as a rigid rule when neither the WHO guidance nor NHS guidance is quite so rigid.
The WHO guidance clarified that introduction of solid foods for babies under 17 weeks of age carried risks and that introducing solid foods before six months was unnecessary and for exclusively breastfed babies delaying until six months may carry some benefits in reduction of gastrointestinal infection.
The benefits of delaying after 17 weeks are less clear cut for formula fed babies however there is still no need or benefit to solid food at this age.
Basically the OP is doing something unnecessary but not as far as we know dangerous and certainly not something proven to cause long term gastrointestinal issues like IBS. Would be different if she was feeding cereal to her 12 week old.
Personally I'd not bother feeding purées to a four month old as it's pointless but it's not a crime or likely to cause him any long term harm,
OP if you wish to continue I'd stick at one meal a day as it's unlikely to replace much more important milk then, offer only simple fruit and vegetable purees or fruit and veg as finger foods if he able to eat them, stepping up rapidly at six months to finger foods with iron and zinc which is after all the point of solids to offer these nutrients which are scarcer in milk to babies who are beginning to need them.