So, if that 0.1 BTC was received as 5 separate payments of:
- 0.0301 BTC
- 0.0039 BTC
- 0.0408 BTC
- 0.0019 BTC
- 0.0233 BTC
Then you can just use the two smallest outputs (0.0301 BTC + 0.0019 BTC = 0.0058 BTC) to fund your transaction. In this way, the entity will see no link at all to the three larger outputs under your control.
Or, if you prefer, you could use just the 0.0233 BTC output to fund the transaction, significantly reducing the visibility from the full 0.1 BTC to just 23% of your balance.
Speaking out of personal experience. If you have multiple people you often send Bitcoin to, after only a few Transactions it becomes really hard to keep track of what is going on. This is why I use Monero. It sometimes costs me a lot more than just tracking my Bitcoin Transactions and UTXOs, but after making a few costly mistakes you realize it is worth the cost.
My personal advice for any body willing to maximize their Privacy is use Monero in parallel with Bitcoin. I use my main Bitcoin Seed for Bitcoin only I know about and I use Monero as an intermediary to avoid linking my personal Bitcoin to the Bitcoin I have to spend.
If I link the two smallest Outputs, 0.0039 plus 0.0019 which is in total 0.0058 but only spend 0.005 out of it to pay OP, I now have an UTXO of 0.0008 labeled 'takuma sato' in my Electrum. Then I spend 0.02 out of my 0.0301 on drinks and have an UTXO labeled 'liquor store' containing 0.0101 Bitcoin. Then I decide to finally link my 0.0408 with my 0.0233 to spend 0.06 Bitcoin on a phone. I now have three UTXOs.
0.0008 Bitcoin 'takuma sato'
0.0101 Bitcoin 'liquor store'
0.0041 Bitcoin 'phone store'
Now I have two options. First is easiest. I link the second and third UTXO because I do not care if two stores know I bought something off them. But that is a Privacy concern to me and I would not want takuma sato to know I purchased any thing from the liquor store or the phone store either. So what do I do?
First option is I continue to use my UTXOs separately. I have 0.0149 Bitcoin left but I can not purchase something worth the entire Balance without compromising my Privacy. If I want to purchase another phone worth 0.01 Bitcoin, I can not without linking UTXOs from the two stores. Unless I get more Bitcoin and have an unused UTXO that I can use in combination with the UTXO labeled 'phone store'.
So here comes my second option. Finding a way to remove my identity off the UTXOs I own. The best way to do it is using Monero as an intermediary. Exchange UTXOs from Bitcoin to Monero in chunks of each label category at random times in random separate days. From 0.0149 Bitcoin you exchanged into X Monero. Now return to Bitcoin and split it into multiple Addresses. Say three.
Now you own three anonymized UTXOs of approximately 0.005 Bitcoin. No more labels, no more worries. Costs a little bit more, but it is the cost of Privacy unfortunately. For someone as paranoid as me, it is worth the costs.
Yeah, you have to do a lot of work to keep any reasonable privacy, and if you try to sell your coins in a KYC exchange for fiat it will be hell to explain where the funds came from. Just to exercise any reasonable amount of privacy (as in, the same privacy one would have when you are sending a regular bank transfer, that is, sending money without revealing your funds in the process) you get labeled a suspicious individual. This is why I don't see any way to cash out Bitcoin unless you mined it and send it directly to the exchange, or bought it from a KYC exchange and has a ticket. Anything else starts becoming too convoluted.
This also showcases how BTC will never be used at a mainstream level, at least until one can achieve similar level of privacy of a bank transfer (again, not potentially revealing your funds with a transaction) by just clicking a send button. Im not familiar with LN and have no idea how it works but nobody uses it that I know, when someone lists an item or service they usually just have regular bc1 addresses.