What is the secret behind the use of the restrictive form in the Hadith, "He does not learn it except to gain thereby a worldly عرضًا (a material gain/benefit)," and is it understood from this that it is permissible to share the intention in seeking knowledge between this world and the Hereafter? And is it permissible for a financial reward to be an incentive for seeking شرعي (Islamic legal) knowledge without that leading to sharing the intention?

Whoever learns knowledge for the sake of Allah and not to gain a worldly عرض from it, will not find the scent of Paradise on the Day of Resurrection. The essence of taking means, such as obtaining a certificate or entering competitions, lies in the intention. So, whoever's intention is solely to seek this world, will have a share of the warning. As for whoever's intention is to benefit people and spread knowledge, any worldly benefits they acquire are considered an expedited reward and do not diminish their recompense.