Firstly let me give a generic background. Before diving into answering your question.

Dukkha appears in many contexts and granularity when discussing Buddhism. In the level you seem to be discussing this at the level of perception. The most relevant Suttas are the ones dealing with as a perception. There couple of such Suttas but a well translated one is: (Vitthāra) Satta Sañña Sutta, Meghiya Sutta.

Also Dukkha being the 1st Noble Truth this comes to relevance.

You should look at impermanence, the perception of suffering in the impermanent, the perception of a lack of self in the suffering.

As I practice more and more on seeing life as Dukkha, something interesting happens. I feel a greater sense of gratitude and contentment.

The 1st Noble truth is called Noble because once you start observing Dukkha objectively this leads to you becoming Noble person free from any form of suffering. This is perhaps what you are experiencing.

First one must accept the fact of suffering. Everywhere suffering exists; this is a universal truth. But it becomes a noble truth when one starts observing it without reacting, because anyone who does so is bound to become a noble, saintly person.

When one starts observing the First Noble Truth, the truth of suffering, then very quickly the cause of suffering becomes clear, and one starts observing it also; this is the Second Noble Truth. If the cause is eradicated, then suffering is eradicated; this is the Third Noble Truth—the eradication of suffering. To achieve its eradication one must take steps; this is the Fourth Noble Truth—the way to end suffering by eradicating its cause.

Source: The Discourse Summaries (day 5) by S. N. Goenka

If I am to presume that you are still a beginner in meditation you are dealing with Dukkha at some conceptual level than seeing it directly at an experiential level. What needs to be done here is when some visitute or lifes pops up and also some unwanted thing happens or some wanted thing does not happen look at it as "this situation will not last forever, this will also pass, this is impermanent". And if it is something pleasant look at it as "this is pleasant but all good things will come to an end, am I ready to give ups then this ends". Thereby you are understanding impermanence nature of experience even when positive.

See additional information in the above source.

I am not talking about seeing things as they are directly and non-conceptually, piercing through and seeing emptiness. I am a beginner, stuck in concepts. But the more I interpret my existence in view of impermanence/anicca, suffering/dukkha, and non-self/anattā, the more grateful and content I become.

To piercing through to see you need to pratice regularly until your are sensitive in the whole body, i.e., you can feel sensation throughout your body. (If you are doing Breath meditation then the whole cycle of the breath with it touching and flowing and the sensations on the concentration spot.) Once you get that then you will start seeing the arising and passing of phenomena in some parts of the body. Some further pratice the whole body. The secret of getting here is practice regularly and also taking intensive residential courses.

Once you realise impermanence then others follow 1st at the perceptional level. I.e. "If this thing that is present will come to an end then it is unsatisfactory. If I cannot control or influence what is unsatisfactory to disappear or prolong what is satisfactory I have not control and there is nothing worth considering as self."

However, merely to feel the sensations within is not enough to remove our delusions. Instead, it is essential to understand the ti-lakkhaṇā (three characteristics) of all phenomena. We must directly experience anicca (impermanence), dukkha (suffering), and anatta (selflessness) within ourselves. Of these three, the Buddha always stressed the importance of anicca because the realization of the other two will easily follow when we experience deeply the characteristic of impermanence. In the Meghiya Sutta of the Udāna he said:

Aniccasaññino hi, Meghiya, anattasaññā saṇṭhāti, anattasaññī asmimānasamugghātaṃ pāpuṇāti diṭṭheva dhamme nibbānaṃ.7

In one, Meghiya, who perceives impermanence, the perception of selflessness is established. One who perceives what is selfless wins the uprooting of the pride of egotism in this very life, and thus realizes nibbāna.

Therefore, in the practice of satipaṭṭhāna, the experience of anicca, arising and passing away, plays a crucial role. This experience of anicca as it manifests in the mind and body is also called vipassanā. The practice of Vipassana is the same as the practice of satipaṭṭhāna.

Source: Vedanā in the Practice of Satipaṭṭhāna

Am I "fooling" myself? Is it just another aspect of Dukkha, like when you are in love and don't see that it's going to end/change?

Everyone is fooled. We are also ways fooled by stimuli which is in short ignorance (or miss identifying or perceiving what is felt). We choose not to see that it will end. We attach a false sense of permanence. These are distortions of reality. (Vipallasa Sutta)