It is important to note that celebrating anniversaries is a non-Muslim practice and a product of Western culture. The Prophet Muhammad (peace be upon him) instructed us to avoid imitating non-Muslims. Celebrating anniversaries, cutting cakes, and congratulating each other on anniversaries are all practices that are part of non-Muslim cultures. Therefore, following the Prophet’s teachings, one should refrain from such customs and traditions.
If, hypothetically, someone who genuinely detests the customs and traditions of non-Muslims, on the occasion of an anniversary, holds a simple celebration at home free from the abominations prevalent in typical anniversary celebrations, with the intention of thanking Allah the Almighty for granting him a year filled with health and the tawfiq to perform acts of worship, then some scholars, including Hazrat Gangohi (May Allah have mercy on him), have deemed it permissible with the restrictions mentioned above.
However, it is no secret that nobody in our societies celebrates anniversaries with these pure intentions while also abiding by these restrictions, therefore the fatwa regarding this issue is that it is not permissible to celebrate anniversaries due to the prevalence of societal evils.
The answer to your questions lies in the details stated above. There is room for a man to give his wife a gift or to take her out for dinner as a token of gratitude or to strengthen their mutual relationship, provided he avoids all the abominations associated with typical anniversary celebrations. That being said, this practice should not be made a regular routine or be considered mandatory. Therefore, if this gesture is occasionally neglected and sometimes not done on the exact day of the anniversary, rather a day before or after it, it will not be called impermissible.